Clelland, Jeanne N.; Klotz, Taylor Beltrami fields with nonconstant proportionality factor. (English) Zbl 1444.53018 Arch. Ration. Mech. Anal. 236, No. 2, 767-800 (2020). MSC: 53A45 58A15 53-01 PDF BibTeX XML Cite \textit{J. N. Clelland} and \textit{T. Klotz}, Arch. Ration. Mech. Anal. 236, No. 2, 767--800 (2020; Zbl 1444.53018) Full Text: DOI arXiv
Hwang, Jun-Muk An application of Cartan’s equivalence method to Hirschowitz’s conjecture on the formal principle. (English) Zbl 1472.32010 Ann. Math. (2) 189, No. 3, 979-1000 (2019). Reviewer: Zakarias Sjöström Dyrefelt (Trieste) MSC: 32K07 58A15 32C22 PDF BibTeX XML Cite \textit{J.-M. Hwang}, Ann. Math. (2) 189, No. 3, 979--1000 (2019; Zbl 1472.32010) Full Text: DOI arXiv
McKay, Benjamin Introduction to exterior differential systems. (English) Zbl 1420.58001 Gutt, Jan (ed.) et al., Geometry of Lagrangian Grassmannians and nonlinear PDEs, Warsaw, Poland, September 5–9, 2016. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 117, 45-55 (2019). Reviewer: Masoud Sabzevari (Shahr-e Kord) MSC: 58A15 PDF BibTeX XML Cite \textit{B. McKay}, Banach Cent. Publ. 117, 45--55 (2019; Zbl 1420.58001) Full Text: DOI arXiv
Hinkkanen, Aimo Another look at the complex dilatation. (English) Zbl 1362.30029 J. Anal. 24, No. 2, 277-291 (2016). MSC: 30C62 PDF BibTeX XML Cite \textit{A. Hinkkanen}, J. Anal. 24, No. 2, 277--291 (2016; Zbl 1362.30029) Full Text: DOI
Ivey, Thomas A.; Landsberg, Joseph M. Cartan for beginners. Differential geometry via moving frames and exterior differential systems. 2nd edition. (English) Zbl 1361.53001 Graduate Studies in Mathematics 175. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-0986-9/hbk; 978-1-4704-3591-2/ebook). xviii, 453 p. (2016). Reviewer: Gabriel Eduard Vilcu (Ploieşti) MSC: 53-01 53A05 58A15 53A20 53C10 53C05 34C41 PDF BibTeX XML Cite \textit{T. A. Ivey} and \textit{J. M. Landsberg}, Cartan for beginners. Differential geometry via moving frames and exterior differential systems. 2nd edition. Providence, RI: American Mathematical Society (AMS) (2016; Zbl 1361.53001) Full Text: DOI
Salač, Tomáš \(k\)-Dirac operator and the Cartan-Kähler theorem for weighted differential operators. (English) Zbl 1354.58002 Differ. Geom. Appl. 49, 351-371 (2016). MSC: 58A15 35F46 58A20 58A30 PDF BibTeX XML Cite \textit{T. Salač}, Differ. Geom. Appl. 49, 351--371 (2016; Zbl 1354.58002) Full Text: DOI arXiv
Weingart, Gregor An introduction to exterior differential systems. (English) Zbl 1331.58005 Herrera, Rafael (ed.) et al., Geometry of manifolds with non-negative sectional curvature. Selected lecture notes based on the presentations at the 3rd mini-meeting on differential geometry “Recent advances in the geometry of manifolds with non-negative sectional curvature”, Guanajuato, México, December 6–17, 2010. Cham: Springer (ISBN 978-3-319-06372-0/pbk; 978-3-319-06373-7/ebook). Lecture Notes in Mathematics 2110, 117-196 (2014). Reviewer: Benjamin McKay (Cork) MSC: 58A15 58A20 PDF BibTeX XML Cite \textit{G. Weingart}, Lect. Notes Math. 2110, 117--196 (2014; Zbl 1331.58005) Full Text: DOI
Salač, Tomáš \(k\)-Dirac operator and the Cartan-Kähler theorem. (English) Zbl 1313.58001 Arch. Math., Brno 49, No. 5, 333-346 (2013). MSC: 58A17 53C27 58A15 PDF BibTeX XML Cite \textit{T. Salač}, Arch. Math., Brno 49, No. 5, 333--346 (2013; Zbl 1313.58001) Full Text: DOI arXiv
Noda, Takahiro; Shibuya, Kazuhiro Second order type-changing equations for a scalar function on a plane. (English) Zbl 1246.35137 Osaka J. Math. 49, No. 1, 101-124 (2012). Reviewer: Benjamin McKay (Cork) MSC: 35N10 35M10 58A20 PDF BibTeX XML Cite \textit{T. Noda} and \textit{K. Shibuya}, Osaka J. Math. 49, No. 1, 101--124 (2012; Zbl 1246.35137) Full Text: Euclid
Kahouadji, Nabil Construction of local conservation laws by generalized isometric embeddings of vector bundles. (English) Zbl 1248.58003 Asian J. Math. 15, No. 4, 521-538 (2011). Reviewer: Benjamin McKay (Cork) MSC: 58A15 37K05 32C22 PDF BibTeX XML Cite \textit{N. Kahouadji}, Asian J. Math. 15, No. 4, 521--538 (2011; Zbl 1248.58003) Full Text: DOI arXiv Euclid
Bryant, Robert L. Non-embedding and non-extension results in special holonomy. (English) Zbl 1221.53084 García-Prada, Oscar (ed.) et al., The many facets of geometry. A tribute to Nigel Hitchin. Oxford: Oxford University Press (ISBN 978-0-19-953492-0/hbk). 346-367 (2010). Reviewer: Simon Chiossi (Torino) MSC: 53C29 PDF BibTeX XML Cite \textit{R. L. Bryant}, in: The many facets of geometry. A tribute to Nigel Hitchin. Oxford: Oxford University Press. 346--367 (2010; Zbl 1221.53084) Full Text: arXiv
Carlson, James; Green, Mark; Griffiths, Phillip Variations of Hodge structure considered as an exterior differential system: old and new results. (English) Zbl 1187.14001 SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 087, 40 p. (2009). MSC: 14-02 14C30 PDF BibTeX XML Cite \textit{J. Carlson} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 5, Paper 087, 40 p. (2009; Zbl 1187.14001) Full Text: DOI arXiv EuDML EMIS
Leśniak, Zbigniew On the existence of analytic solutions of the d’Alembert equation. (English) Zbl 1170.35312 Int. J. Pure Appl. Math. 48, No. 3, 385-397 (2008). MSC: 35A30 35L25 35C05 58A17 58A20 PDF BibTeX XML Cite \textit{Z. Leśniak}, Int. J. Pure Appl. Math. 48, No. 3, 385--397 (2008; Zbl 1170.35312)
Xie, Zheng; Li, Hongbo Exterior difference system on hypercubic lattice. (English) Zbl 1137.39014 Acta Appl. Math. 99, No. 1, 97-116 (2007). Reviewer: Marian Ioan Munteanu (Iaşi) MSC: 39A12 58A15 81T75 03G10 39A70 PDF BibTeX XML Cite \textit{Z. Xie} and \textit{H. Li}, Acta Appl. Math. 99, No. 1, 97--116 (2007; Zbl 1137.39014) Full Text: DOI
Kamran, Niky Exterior differential systems and Cartan-Kähler theory. (English) Zbl 1078.58003 Acta Appl. Math. 87, No. 1-3, 147-164 (2005). Reviewer: Wing-Sum Cheung (Hong Kong) MSC: 58A15 PDF BibTeX XML Cite \textit{N. Kamran}, Acta Appl. Math. 87, No. 1--3, 147--164 (2005; Zbl 1078.58003) Full Text: DOI
Ivey, Thomas A.; Landsberg, J. M. Cartan for beginners: Differential geometry via moving frames and exterior differential systems. (English) Zbl 1105.53001 Graduate Studies in Mathematics 61. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3375-8/hbk). xiv, 378 p. (2003). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 53-01 58A15 53A20 53C10 53C05 34C41 PDF BibTeX XML Cite \textit{T. A. Ivey} and \textit{J. M. Landsberg}, Cartan for beginners: Differential geometry via moving frames and exterior differential systems. Providence, RI: American Mathematical Society (AMS) (2003; Zbl 1105.53001)
Ekeland, Ivar Two problems in economics. (English) Zbl 1028.91014 Jahresber. Dtsch. Math.-Ver. 104, No. 2, 51-58 (2002). Reviewer: V.Postolică (Piatra Neamt) MSC: 91B08 PDF BibTeX XML Cite \textit{I. Ekeland}, Jahresber. Dtsch. Math.-Ver. 104, No. 2, 51--58 (2002; Zbl 1028.91014)
Mehdi, M. Existence of conservation laws in nilpotent case. (English) Zbl 0940.35050 Acta Math. Univ. Comen., New Ser. 68, No. 2, 243-247 (1999). Reviewer: Jan Chrastina (Brno) MSC: 35F20 37J99 35N10 58A17 58J60 PDF BibTeX XML Cite \textit{M. Mehdi}, Acta Math. Univ. Comen., New Ser. 68, No. 2, 243--247 (1999; Zbl 0940.35050) Full Text: EuDML EMIS
Grifone, Joseph; Muzsnay, Zoltán Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope. (On the inverse problem of the variational calculus: existence of Lagrangians associated with a spray in the isotropic case.). (French) Zbl 0939.58023 Ann. Inst. Fourier 49, No. 4, 1387-1421 (1999). Reviewer: N.Papaghiuc (Iaşi) MSC: 58E30 35N10 53B05 53C21 53C60 PDF BibTeX XML Cite \textit{J. Grifone} and \textit{Z. Muzsnay}, Ann. Inst. Fourier 49, No. 4, 1387--1421 (1999; Zbl 0939.58023) Full Text: DOI Numdam EuDML
Kamran, Niky; Robart, Thierry A compatible analytic manifold structure for Lie pseudogroups of infinite type. (English) Zbl 0949.58023 Henneaux, Marc (ed.) et al., Secondary calculus and cohomological physics. Proceedings of a conference, Moscow, Russia, August 24-31, 1997. Providence, RI: AMS, American Mathematical Society. Contemp. Math. 219, 111-120 (1998). Reviewer: A.L.Onishchik (Yaroslavl) MSC: 58H05 22E65 17B65 PDF BibTeX XML Cite \textit{N. Kamran} and \textit{T. Robart}, Contemp. Math. 219, 111--120 (1998; Zbl 0949.58023)
Grifone, Joseph; Mehdi, Mohamad Existence of conservation laws and characterization of recursion operators for completely integrable systems. (English) Zbl 0888.35025 Trans. Am. Math. Soc. 349, No. 11, 4609-4633 (1997). MSC: 35G20 37J35 37K10 58J60 35N10 PDF BibTeX XML Cite \textit{J. Grifone} and \textit{M. Mehdi}, Trans. Am. Math. Soc. 349, No. 11, 4609--4633 (1997; Zbl 0888.35025) Full Text: DOI
Szilasi, J.; Muzsnay, Z. Nonlinear connections and the problem of metrizability. (English) Zbl 0799.53031 Publ. Math. Debr. 42, No. 1-2, 175-192 (1993). Reviewer: R.Miron (Iaşi) MSC: 53C05 53C60 PDF BibTeX XML Cite \textit{J. Szilasi} and \textit{Z. Muzsnay}, Publ. Math. Debr. 42, No. 1--2, 175--192 (1993; Zbl 0799.53031)
Hartley, David; Tucker, Robin W. A constructive implementation of the Cartan-Kähler theory of exterior differential systems. (English) Zbl 0753.58002 J. Symb. Comput. 12, No. 6, 655-667 (1991). Reviewer: F.C.Klepp (Timişoara) MSC: 58A15 68Q25 58J99 35L05 PDF BibTeX XML Cite \textit{D. Hartley} and \textit{R. W. Tucker}, J. Symb. Comput. 12, No. 6, 655--667 (1991; Zbl 0753.58002) Full Text: DOI
Edelen, Dominic G. B. Alternatives to the Cartan-Kähler theorem. (English) Zbl 0718.58010 Nonlinear Anal., Theory Methods Appl. 15, No. 8, 765-786 (1990). Reviewer: I.Kolář (Brno) MSC: 58A15 58J60 PDF BibTeX XML Cite \textit{D. G. B. Edelen}, Nonlinear Anal., Theory Methods Appl. 15, No. 8, 765--786 (1990; Zbl 0718.58010) Full Text: DOI
Morimoto, Tohru Théorème de Cartan-Kähler dans une classe de fonctions formelles Gevrey. (Cartan-Kähler theorem in a class of formal Gevrey functions). (French) Zbl 0714.58060 C. R. Acad. Sci., Paris, Sér. I 311, No. 7, 433-436 (1990). Reviewer: A.Dimca MSC: 58J99 58A20 22E25 PDF BibTeX XML Cite \textit{T. Morimoto}, C. R. Acad. Sci., Paris, Sér. I 311, No. 7, 433--436 (1990; Zbl 0714.58060)
Kakié, Kunio Existence of \(C^{\infty}\) integral manifolds of an involutive Pfaffian system. (English) Zbl 0705.58002 Comment. Math. Univ. St. Pauli 39, No. 1, 111-125 (1990). Reviewer: J.Kubarski MSC: 58A17 35A30 58A15 PDF BibTeX XML Cite \textit{K. Kakié}, Comment. Math. Univ. St. Pauli 39, No. 1, 111--125 (1990; Zbl 0705.58002)
Gardner, Robert B. The method of equivalence and its applications. (English) Zbl 0694.53027 CBMS-NSF Regional Conference Series in Applied Mathematics, 58. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. vii, 127 p. $ 21.75 (1989). Reviewer: J.Chrastina MSC: 53C10 58H05 53-02 PDF BibTeX XML Cite \textit{R. B. Gardner}, The method of equivalence and its applications. Philadelphia, PA: Society for Industrial and Applied Mathematics (1989; Zbl 0694.53027)
Tsujishita, Toru Compatibility of systems of super differential equations. (English) Zbl 0699.58005 J. Geom. Phys. 6, No. 2, 169-213 (1989). Reviewer: T.Tsujishita MSC: 58A50 83E50 35N99 PDF BibTeX XML Cite \textit{T. Tsujishita}, J. Geom. Phys. 6, No. 2, 169--213 (1989; Zbl 0699.58005) Full Text: DOI
Bryant, Robert L. Metrics with exceptional holonomy. (English) Zbl 0637.53042 Ann. Math. (2) 126, 525-576 (1987). Reviewer: I.Dotti-Miatello MSC: 53C10 53C20 PDF BibTeX XML Cite \textit{R. L. Bryant}, Ann. Math. (2) 126, 525--576 (1987; Zbl 0637.53042) Full Text: DOI
Chern, Shiingshen; Griffiths, Phillip A. Pfaffian systems in involution. (English) Zbl 0677.58005 Differential geometry and differential equations, Proc. Symp., Changchun/China 1982, 233-256 (1986). Reviewer: A.Stone MSC: 58A17 PDF BibTeX XML
Wilkinson, Steven Exterior differential systems and the problem of characterizing Gauss maps. (English) Zbl 0587.53004 Nonlinear problems in geometry, Proc. AMS Spec. Sess., 820th Meet. AMS, Mobile/Ala. 1985, Contemp. Math. 51, 121-130 (1986). Reviewer: D.Yang MSC: 53A07 58A15 PDF BibTeX XML
Patissier, Guy Caractéristiques des équations analogues à l’équation de Monge- Ampère. (Characteristics of equations analogous to the Monge-Ampère equation). (French) Zbl 0614.58003 J. Math. Pures Appl., IX. Sér. 64, 439-456 (1985). Reviewer: D.Yang MSC: 58A15 PDF BibTeX XML Cite \textit{G. Patissier}, J. Math. Pures Appl. (9) 64, 439--456 (1985; Zbl 0614.58003)
Caviglia, Giacomo Conditions on a tensor of rank (1,3) to be a curvature tensor. (English) Zbl 0532.53010 Boll. Unione Mat. Ital., Suppl. 1983, No. 2, 57-63 (1983). Reviewer: S.Takizawa MSC: 53B05 35A07 PDF BibTeX XML Cite \textit{G. Caviglia}, Boll. Unione Mat. Ital., Suppl. 1983, No. 2, 57--63 (1983; Zbl 0532.53010)