Song, Xue; Li, Enze; Pei, Donghe Legendrian dualities and evolute-involute curve pairs of spacelike fronts in null sphere. (English) Zbl 1496.53016 J. Geom. Phys. 178, Article ID 104543, 11 p. (2022). MSC: 53A35 53A04 53A05 57R45 PDF BibTeX XML Cite \textit{X. Song} et al., J. Geom. Phys. 178, Article ID 104543, 11 p. (2022; Zbl 1496.53016) Full Text: DOI OpenURL
Giardino, Sergio A primer on the differential geometry of quaternionic curves. (English) Zbl 1482.53062 Math. Methods Appl. Sci. 44, No. 18, 14428-14436 (2021). MSC: 53C26 53A04 11R52 PDF BibTeX XML Cite \textit{S. Giardino}, Math. Methods Appl. Sci. 44, No. 18, 14428--14436 (2021; Zbl 1482.53062) Full Text: DOI arXiv OpenURL
Martinez-Maure, Yves Real and complex hedgehogs, their symplectic area, curvature and evolutes. (English) Zbl 1471.52003 J. Symplectic Geom. 19, No. 3, 567-606 (2021). MSC: 52A20 53A07 53D05 32A10 PDF BibTeX XML Cite \textit{Y. Martinez-Maure}, J. Symplectic Geom. 19, No. 3, 567--606 (2021; Zbl 1471.52003) Full Text: DOI OpenURL
Reventós, Agustí [Solé, Josep Lluís] Gaspard Monge. (Catalan. English summary) Zbl 1426.01018 Butll. Soc. Catalana Mat. 33, No. 2, 111-145 (2018). Reviewer: Robert W. van der Waall (Amsterdam) MSC: 01A70 01A50 53A04 53-03 PDF BibTeX XML Cite \textit{A. Reventós}, Butll. Soc. Catalana Mat. 33, No. 2, 111--145 (2018; Zbl 1426.01018) Full Text: DOI OpenURL
Craizer, Marcos; Saia, Marcelo J.; Sánchez, Luis F. Affine focal sets of codimension-2 submanifolds contained in hypersurfaces. (English) Zbl 1407.53011 Proc. R. Soc. Edinb., Sect. A, Math. 148, No. 5, 995-1016 (2018). Reviewer: Atsushi Fujioka (Osaka) MSC: 53A15 PDF BibTeX XML Cite \textit{M. Craizer} et al., Proc. R. Soc. Edinb., Sect. A, Math. 148, No. 5, 995--1016 (2018; Zbl 1407.53011) Full Text: DOI arXiv OpenURL
Balestro, Vitor; Martini, Horst; Teixeira, Ralph On Legendre curves in normed planes. (English) Zbl 1408.46017 Pac. J. Math. 297, No. 1, 1-27 (2018). MSC: 46B20 51L10 52A21 53A04 53A35 PDF BibTeX XML Cite \textit{V. Balestro} et al., Pac. J. Math. 297, No. 1, 1--27 (2018; Zbl 1408.46017) Full Text: DOI arXiv OpenURL
Öztürk, Günay; Arslan, Kadri; Bulca, Betül A characterization of involutes and evolutes of a given curve in \(\mathbb{E}^n\). (English) Zbl 1398.53009 Kyungpook Math. J. 58, No. 1, 117-135 (2018). MSC: 53A04 53A05 PDF BibTeX XML Cite \textit{G. Öztürk} et al., Kyungpook Math. J. 58, No. 1, 117--135 (2018; Zbl 1398.53009) Full Text: DOI arXiv OpenURL
Scalco Dias, Fabio; Tari, Farid On vertices and inflections of plane curves. (English) Zbl 1388.53003 J. Singul. 17, 70-80 (2018). MSC: 53A04 58K05 58K60 PDF BibTeX XML Cite \textit{F. Scalco Dias} and \textit{F. Tari}, J. Singul. 17, 70--80 (2018; Zbl 1388.53003) Full Text: DOI OpenURL
Craizer, Marcos; Teixeira, Ralph; Balestro, Vitor Closed cycloids in a normed plane. (English) Zbl 1382.52002 Monatsh. Math. 185, No. 1, 43-60 (2018). MSC: 52A21 52A10 53A15 53A40 51L15 PDF BibTeX XML Cite \textit{M. Craizer} et al., Monatsh. Math. 185, No. 1, 43--60 (2018; Zbl 1382.52002) Full Text: DOI arXiv OpenURL
Babaarslan, Murat; Yayli, Yusuf On space-like constant slope surfaces and Bertrand curves in Minkowski 3-space. (English) Zbl 1399.53020 An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 63, No. 2, 323-338 (2017). MSC: 53B25 PDF BibTeX XML Cite \textit{M. Babaarslan} and \textit{Y. Yayli}, An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 63, No. 2, 323--338 (2017; Zbl 1399.53020) Full Text: arXiv OpenURL
Reeve, Graham Mark; Tari, Farid Minkowski symmetry sets of plane curves. (English) Zbl 1432.53016 Proc. Edinb. Math. Soc., II. Ser. 60, No. 2, 461-480 (2017). MSC: 53A35 53B30 57R45 PDF BibTeX XML Cite \textit{G. M. Reeve} and \textit{F. Tari}, Proc. Edinb. Math. Soc., II. Ser. 60, No. 2, 461--480 (2017; Zbl 1432.53016) Full Text: DOI OpenURL
Nolasco, Boaventura; Pacheco, Rui Evolutes of plane curves and null curves in Minkowski 3-space. (English) Zbl 1365.53009 J. Geom. 108, No. 1, 195-214 (2017). MSC: 53A35 53A04 53B30 PDF BibTeX XML Cite \textit{B. Nolasco} and \textit{R. Pacheco}, J. Geom. 108, No. 1, 195--214 (2017; Zbl 1365.53009) Full Text: DOI arXiv OpenURL
Hayashi, Ryota; Izumiya, Shyuichi; Sato, Takami Focal surfaces and evolutes of curves in hyperbolic space. (English) Zbl 1364.53011 Commun. Korean Math. Soc. 32, No. 1, 147-163 (2017). Reviewer: N. K. Stephanidis (Thessaloniki) MSC: 53A25 58K35 53A07 PDF BibTeX XML Cite \textit{R. Hayashi} et al., Commun. Korean Math. Soc. 32, No. 1, 147--163 (2017; Zbl 1364.53011) Full Text: DOI Link OpenURL
Craizer, Marcos; Martini, Horst Involutes of polygons of constant width in Minkowski planes. (English) Zbl 1354.52003 Ars Math. Contemp. 11, No. 1, 107-125 (2016). MSC: 52A10 52A21 53A15 53A40 51B20 PDF BibTeX XML Cite \textit{M. Craizer} and \textit{H. Martini}, Ars Math. Contemp. 11, No. 1, 107--125 (2016; Zbl 1354.52003) Full Text: DOI arXiv OpenURL
Fukunaga, Tomonori; Takahashi, Masatomo Involutes of fronts in the Euclidean plane. (English) Zbl 1352.58007 Beitr. Algebra Geom. 57, No. 3, 637-653 (2016). Reviewer: Aleksandr G. Aleksandrov (Moskva) MSC: 58K05 53A04 57R45 PDF BibTeX XML Cite \textit{T. Fukunaga} and \textit{M. Takahashi}, Beitr. Algebra Geom. 57, No. 3, 637--653 (2016; Zbl 1352.58007) Full Text: DOI Link OpenURL
Cufí, Julià; Reventós, Agustí Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature. (English) Zbl 1340.53004 Arch. Math., Brno 50, No. 4, 219-236 (2014). Reviewer: Josef Janyška (Brno) MSC: 53A04 52A55 52A10 PDF BibTeX XML Cite \textit{J. Cufí} and \textit{A. Reventós}, Arch. Math., Brno 50, No. 4, 219--236 (2014; Zbl 1340.53004) Full Text: DOI arXiv OpenURL
Bukcu, Bahaddin; Karacan, Murat Kemal On involute and evolute curves of spacelike curve with a spacelike principal normal in Minkowski 3-space. (English) Zbl 1192.53002 Int. J. Math. Comb. 1, 27-37 (2009). MSC: 53A04 53B30 53A35 PDF BibTeX XML Cite \textit{B. Bukcu} and \textit{M. K. Karacan}, Int. J. Math. Comb. 2009, No. 1, 27--37 (2009; Zbl 1192.53002) OpenURL
Izumiya, Shyuichi; Takahashi, Masatomo Caustics and wave front propagations: applications to differential geometry. (English) Zbl 1156.57025 Janeczko, Stanisław (ed.) et al., Geometry and topology of caustics — Caustics ’06. Proceedings of the 3rd Banach Center symposium, Warsaw, Poland, June 19–30, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 82, 125-142 (2008). Reviewer: Dorin Andrica (Cluj-Napoca) MSC: 57R45 58K99 53C40 PDF BibTeX XML Cite \textit{S. Izumiya} and \textit{M. Takahashi}, Banach Cent. Publ. 82, 125--142 (2008; Zbl 1156.57025) Full Text: Link OpenURL
Izumiya, Shyuichi; Takahashi, Masatomo Spacelike parallels and evolutes in Minkowski pseudo-spheres. (English) Zbl 1121.53036 J. Geom. Phys. 57, No. 8, 1569-1600 (2007). Reviewer: Serguey M. Pokas (Odessa) MSC: 53C40 53C50 57R45 58K99 53A35 PDF BibTeX XML Cite \textit{S. Izumiya} and \textit{M. Takahashi}, J. Geom. Phys. 57, No. 8, 1569--1600 (2007; Zbl 1121.53036) Full Text: DOI OpenURL
Bukcu, Bahaddin; Karacan, Murat Kemal On the involute and evolute curves of the spacelike curve with a spacelike binormal in Minkowski 3-space. (English) Zbl 1123.53004 Int. J. Contemp. Math. Sci. 2, No. 5-8, 221-232 (2007). Reviewer: Hans Sachs (Leoben) MSC: 53A04 53B30 53A35 PDF BibTeX XML Cite \textit{B. Bukcu} and \textit{M. K. Karacan}, Int. J. Contemp. Math. Sci. 2, No. 5--8, 221--232 (2007; Zbl 1123.53004) Full Text: DOI Link OpenURL
Müller, Stephanie; Schwenk-Schellschmidt, Angela; Simon, Udo Eigenvalue equations in curve theory. II: Evolutes and involutes. (English) Zbl 1137.53003 Result. Math. 50, No. 1-2, 109-124 (2007). MSC: 53A04 34A30 34L15 53A17 PDF BibTeX XML Cite \textit{S. Müller} et al., Result. Math. 50, No. 1--2, 109--124 (2006; Zbl 1137.53003) Full Text: DOI OpenURL
Adhikari, Swapan Kumar Mechanical role of crucial ligaments in flexion and extension expressed geometrically. (English) Zbl 1114.74033 Facta Univ., Ser. Mech. Autom. Control Robot. 4, No. 17, 367-372 (2005). Reviewer: Katica Hedrih (Niš) MSC: 74L15 92C10 PDF BibTeX XML Cite \textit{S. K. Adhikari}, Facta Univ., Ser. Mech. Autom. Control Robot. 4, No. 17, 367--372 (2005; Zbl 1114.74033) OpenURL
Audin, Michèle Geometry. Transl. from the French. (English) Zbl 1043.51001 Universitext. Berlin: Springer (ISBN 3-540-43498-4/pbk). vi, 357 p. (2003). Reviewer: Serguey M. Pokas (Odessa) MSC: 51-01 53A04 53A05 51Nxx 53-01 PDF BibTeX XML Cite \textit{M. Audin}, Geometry. Transl. from the French. Berlin: Springer (2003; Zbl 1043.51001) Full Text: DOI OpenURL
Gollek, Hubert Natural algebraic representation formulas for curves in \({\mathbb C}^3\). (English) Zbl 1029.53012 Opozda, Barbara (ed.) et al., PDEs, submanifolds and affine differential geometry. Contributions of a conference, Warsaw, Poland, September 4-10, 2000. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 57, 109-134 (2002). Reviewer: Wayne Rossman (Kobe) MSC: 53A10 49Q05 30F30 PDF BibTeX XML Cite \textit{H. Gollek}, Banach Cent. Publ. 57, 109--134 (2002; Zbl 1029.53012) Full Text: Link OpenURL
Gibson, C. G. Elementary geometry of differentiable curves: an undergraduate introduction. (English) Zbl 1031.53002 Cambridge: Cambridge University Press. xvii, 216 p. (2001). Reviewer: Serguey M.Pokas (Odessa) MSC: 53-01 53A04 00A06 PDF BibTeX XML Cite \textit{C. G. Gibson}, Elementary geometry of differentiable curves: an undergraduate introduction. Cambridge: Cambridge University Press (2001; Zbl 1031.53002) OpenURL
Rutter, John W. Geometry of curves. (English) Zbl 0962.53002 Chapman and Hall Mathematics Series. Boca Raton, FL: Chapman & Hall/CRC Press. xviii, 361 p. (2000). Reviewer: Aleksandar Perović (Berlin) MSC: 53-01 51N05 14H50 53A04 68U05 PDF BibTeX XML Cite \textit{J. W. Rutter}, Geometry of curves. Boca Raton, FL: Chapman \& Hall/CRC Press (2000; Zbl 0962.53002) OpenURL
Audin, Michèle Geometry. (Géométrie.) (French) Zbl 1017.51002 Collection Mathématiques. Paris: Belin. Montpellier: Espaces 34. 320 p. (1998). MSC: 51-XX PDF BibTeX XML Cite \textit{M. Audin}, Géométrie. Paris: Belin; Montpellier: Espaces 34 (1998; Zbl 1017.51002) OpenURL
Schaaf, J. A.; Ravani, B. Geometric continuity of ruled surfaces. (English) Zbl 0903.68192 Comput. Aided Geom. Des. 15, No. 3, 289-310 (1998). MSC: 68U05 PDF BibTeX XML Cite \textit{J. A. Schaaf} and \textit{B. Ravani}, Comput. Aided Geom. Des. 15, No. 3, 289--310 (1998; Zbl 0903.68192) Full Text: DOI OpenURL
Romero-Fuster, M. C.; Sanabria Codesal, E. A note on inverse invariants of curves. (English) Zbl 0941.53005 Pereira do Vale, A. (ed.) et al., Proceedings of the 1st international meeting on geometry and topology, Braga, Portugal, September 11-13, 1997. Braga: Univ. do Minho, Centro de Matemática, 185-189 (1997). Reviewer: Bernd Wegner (Berlin) MSC: 53A04 53A30 PDF BibTeX XML Cite \textit{M. C. Romero-Fuster} and \textit{E. Sanabria Codesal}, in: Proceedings of the 1st international meeting on geometry and topology, Braga, Portugal, September 11--13, 1997. Braga: Univ. do Minho, Centro de Matemática. 185--189 (1997; Zbl 0941.53005) Full Text: EMIS OpenURL
Josse, Alfrederic Halphen transform. (Transformation d’Halphen.) (French) Zbl 0848.14014 Commun. Algebra 23, No. 12, 4343-4364 (1995). Reviewer: D.Laksov (Stockholm) MSC: 14H20 14N10 PDF BibTeX XML Cite \textit{A. Josse}, Commun. Algebra 23, No. 12, 4343--4364 (1995; Zbl 0848.14014) Full Text: DOI OpenURL
Gray, Alfred Modern differential geometry of curves and surfaces. (Differentialgeometrie. Klassische Theorie in moderner Darstellung. Aus dem Amerikan. übers. u. bearb. von Hubert Gollek.) (German) Zbl 0855.53001 Heidelberg: Spektrum Akademischer Verlag. xix, 618 S. (1994). Reviewer: Bernd Wegner (Berlin) MSC: 53-01 53Axx PDF BibTeX XML Cite \textit{A. Gray}, Differentialgeometrie. Klassische Theorie in moderner Darstellung. Aus dem Amerikan. übers. u. bearb. von Hubert Gollek. Heidelberg: Spektrum Akademischer Verlag (1994; Zbl 0855.53001) OpenURL
van-Brunt, B. Weingarten surfaces. (English) Zbl 0811.53005 Fisher, R. B. (ed.), Design and application of curves and surfaces. Mathematics of surfaces V. Based on the proceedings of the fifth conference on the mathematics of surfaces organized by the Institute of Mathematics and its Applications held in Edinburgh, UK, September 14-16, 1992. Oxford: Clarendon Press. Inst. Math. Appl. Conf. Ser., New Ser. 50, 49-87 (1994). Reviewer: K.Polthier (Berlin) MSC: 53A05 PDF BibTeX XML Cite \textit{B. van-Brunt}, in: Design and application of curves and surfaces. Mathematics of surfaces V. Based on the proceedings of the fifth conference on the mathematics of surfaces organized by the Institute of Mathematics and its Applications held in Edinburgh, UK, September 14-16, 1992. Oxford: Clarendon Press. 49--87 (1994; Zbl 0811.53005) OpenURL
Wegner, Bernd On the evolutes of piecewise linear curves in the plane. (English) Zbl 0723.51008 Rad, Jugosl. Akad. Znan. Umjet. 467, Mat. Znan. 11, 1-16 (1994). Reviewer: Bernd Wegner MSC: 51M20 53A04 PDF BibTeX XML OpenURL
Lee, Chih; Ravani, Bahram; Yang, An Tzu Theory of contact for geometric continuity of parametric curves. (English) Zbl 0754.53008 Visual Comput. 8, No. 5-6, 338-350 (1992). Reviewer: Bernd Wegner (Berlin) MSC: 53A04 68U07 PDF BibTeX XML Cite \textit{C. Lee} et al., Visual Comput. 8, No. 5--6, 338--350 (1992; Zbl 0754.53008) Full Text: DOI OpenURL
Bruce, J. W.; Giblin, P. J. Curves and singularities. 2nd ed. (English) Zbl 0770.53002 Cambridge: Cambridge University Press,. xviii, 321 p. (1992). Reviewer: Bernd Wegner (Berlin) MSC: 53-02 58-02 53A04 53A05 58K35 58C25 58K99 PDF BibTeX XML Cite \textit{J. W. Bruce} and \textit{P. J. Giblin}, Curves and singularities. 2nd ed. Cambridge: Cambridge University Press (1992; Zbl 0770.53002) OpenURL
Manselli, P.; Pucci, C. Uniqueness results for differentiable curves, involutes and evolutes of themselves. (Italian. English summary) Zbl 0761.53002 Boll. Unione Mat. Ital., VII. Ser., A 5, No. 3, 373-379 (1991). Reviewer: Bernd Wegner (Berlin) MSC: 53A04 PDF BibTeX XML Cite \textit{P. Manselli} and \textit{C. Pucci}, Boll. Unione Mat. Ital., VII. Ser., A 5, No. 3, 373--379 (1991; Zbl 0761.53002) OpenURL
Kuyk, Willem; Smits, Lieven On the geometries of the rational unfoldings of \(X^ k\). (English) Zbl 0726.58011 Acta Appl. Math. 19, No. 1, 77-86 (1990). Reviewer: V.G.Angelov (Sofia) MSC: 58K35 92B05 PDF BibTeX XML Cite \textit{W. Kuyk} and \textit{L. Smits}, Acta Appl. Math. 19, No. 1, 77--86 (1990; Zbl 0726.58011) OpenURL
Yoder, Joella G. Unrolling time. Christian Huygens and the mathematization of nature. (English) Zbl 0687.01005 Cambridge: Cambridge University Press. xi, 238 p. £30.00; $ 42.50 (1989). Reviewer: E.J.Aiton MSC: 01A45 01-02 PDF BibTeX XML Cite \textit{J. G. Yoder}, Unrolling time. Christian Huygens and the mathematization of nature. Cambridge: Cambridge University Press (1989; Zbl 0687.01005) OpenURL
Virovere, T. On evolutes of higher order of a normally flat Cartan submanifold \(M_ m\) in \(E_ n\). (Russian. English summary) Zbl 0695.53001 Izv. Akad. Nauk Ehst. SSR, Fiz., Mat. 38, No. 3, 252-256 (1989). Reviewer: Ü.Lumiste MSC: 53A07 PDF BibTeX XML Cite \textit{T. Virovere}, Izv. Akad. Nauk Èst. SSR, Fiz., Mat. 38, No. 3, 252--256 (1989; Zbl 0695.53001) OpenURL
Bruce, James William; Giblin, Peter J. Arnol’d, V. I. (ed.) Curves and singularities. A geometrical introduction to singularity theory. (Krivye i osobennosti. Geometricheskoe vvedenie v teoriyu osobennostej). Transl. from the English by I. G. Shcherbak. Transl. ed. and with a preface by V. I. Arnol’d. (Krivye i osobennosti. Geometricheskoe vvedenie v teoriyu osobennostej.) (Russian) Zbl 0664.58001 Sovremennaya Matematika: Vvodnye Kursy. Moskva: Mir. 264 p. R. 1.20 (1988). MSC: 58C25 58K99 53A04 58-02 53-02 58K35 PDF BibTeX XML Cite \textit{J. W. Bruce} et al., Krivye i osobennosti. Geometricheskoe vvedenie v teoriyu osobennostej (Russian). Transl. from the English by I. G. Shcherbak. Transl. ed. and with a preface by V. I. Arnol'd. Moskva: Mir (1988; Zbl 0664.58001) OpenURL
Bruce, J. W.; Giblin, P. J. Curves and singularities. A geometrical introduction to singularity theory. (English) Zbl 0534.58008 Cambridge etc.: Cambridge University Press. XII, 222 p. hbk: £25.00; $ 39.50; pbk: £8.95; $ 15.95 (1984). Reviewer: A.Dimca MSC: 58C25 58K99 53A04 58K35 58-02 53-02 PDF BibTeX XML OpenURL
Ostrowski, Alexander Collected mathematical papers. Vol. 3: VI: Number theory. VII: Geometry. VIII: Topology. IX: Convergence. (English) Zbl 0527.01020 Basel-Boston-Stuttgart: Birkhäuser Verlag. 532 p. DM 82.00 (1984). MSC: 01A75 01-02 11-03 12-03 40-03 51-03 54-03 PDF BibTeX XML OpenURL
Arnol’d, V. I. Critical points of functions on a manifold with boundary, the simple Lie groups \(B_4\), \(C_k\), and \(F_4\) and singularities of evolutes. (English) Zbl 0415.58004 Russ. Math. Surv. 33, No. 5, 99-116 (1978). MSC: 58C25 58K99 57R45 22E15 PDF BibTeX XML Cite \textit{V. I. Arnol'd}, Russ. Math. Surv. 33, No. 5, 99--116 (1978; Zbl 0415.58004) Full Text: DOI OpenURL
Aoust Integrals of the curves whose involutes by the plan and developed by the plan are all equal. (Intégrales des courbes dont les développantes par le plan et les développées par le plan sont égales entre elles.) (French) JFM 11.0550.02 Bull. S. M. F. VII, 143-154 (1879). Reviewer: Hoppe, Prof. (Berlin) MSC: 53A04 PDF BibTeX XML Cite \textit{Aoust}, Bull. Soc. Math. Fr. 7, 143--154 (1879; JFM 11.0550.02) Full Text: DOI Numdam EuDML OpenURL
Rauscher, V. A study on the relation between evolutes, evolvents, trajectories and envelopes of lines. (Studie über die Beziehungen zwischen Evoluten, Evolventen, Trajectorien und Umhüllungslinien.) (German) JFM 08.0431.03 Wien. Gerold (1876). MSC: 53A04 PDF BibTeX XML OpenURL
Weyr, Em. On the evolutes of plane curves. (Ueber Evolution ebener Curven.) (Czech) JFM 05.0334.01 Casopis II, 277-280 (1873); (Böhmisch). Reviewer: Weyr, Em., Prof. (Prag) MSC: 53A04 PDF BibTeX XML Cite \textit{Em. Weyr}, Čas. Mat. Fys. 2, 277--280 (1873; JFM 05.0334.01) OpenURL
Sidler, G. Trisection of arcs and limacons. (Trisection eines Kreisbogens und die Kreis-Conchoide.) (German) JFM 05.0317.03 Bern. Mitth. 1873 (1873). Reviewer: Scholz, Dr. (Berlin) MSC: 53A04 14H45 PDF BibTeX XML OpenURL