Jüttler, B. Osculating paraboloids of second and third order. (English) Zbl 0868.53012 Abh. Math. Semin. Univ. Hamb. 66, 317-335 (1996). Author’s abstract: “Osculating paraboloids of second order on a surface have been discussed in classical affine differential geometry. We generalize this concept to cubic osculating paraboloids. This yields a visualization of the local properties of a given surface which depend on the derivatives of maximal order four”. Reviewer: Liu Hui-Li (Shenyang) Cited in 2 Documents MSC: 53A15 Affine differential geometry 53-04 Software, source code, etc. for problems pertaining to differential geometry Keywords:osculating surface; Taylor expansion × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Berwald, L., Über affine Geometrie XXX: Die oskulierenden Flächen zweiter Ordnung in der affinen Flä chentheorie, Mathem. Zeitschrift, 10, 160-172 (1921) · JFM 48.0804.02 · doi:10.1007/BF02102313 [2] Blaschke, W., Vorlesungen über Differentialgeometrie II: Affine Differentialgeometrie (1923), Berlin: Springer-Verlag, Berlin · JFM 49.0499.01 [3] Bol, G., Projektive Differentialgeometrie (1954), Göttingen: Vandenhoeck & Ruprecht, Göttingen · Zbl 0059.15501 [4] Darboux, G., Sur le contact des courbes et des surfaces, Bull. des sci. math. etastron., 4, 348-384 (1880) · JFM 12.0590.01 [5] Darboux, G., Sur le contact des coniques et des surfaces, Comptes rendus, 91, 969-972 (1880) · JFM 12.0596.01 [6] Goldman, R.; Sederberg, T.; Anderson, D., Vector Elimination: A technique for the implicitization, inversion and intersection of planar parametric rational polynomial curves, Comp. Aided Geom. Design, 1, 327-356 (1984) · Zbl 0571.65114 · doi:10.1016/0167-8396(84)90020-7 [7] Hoschek, J.; Lasser, D., Fundamentals of Computer Aided Geometric Design (1993), Wellesley: AK Peters, Wellesley · Zbl 0788.68002 [8] Groiss, R.; Kruppa, E., Beiträge zur konstruktiven Flächentheorie, Sitzungsber. Österr. Akad. Wiss. Wien, math.-nat. Klasse (Abt. IIa), 156, 1-48 (1948) · Zbl 0030.26503 [9] Kruppa, E., Analytische und Konstruktive Differentialgeometrie (1957), Wien: Springer-Verlag, Wien · Zbl 0077.15401 [10] Kubota, T., Einige Bemerkungen zur Affinflächentheorie, Science Reports Tokyo, 19, 163-168 (1930) · JFM 56.1199.02 [11] Moutard, Th., Sur le contact des coniques et des surfaces, Comptes rendus, 91, 1055-1058 (1880) · JFM 12.0596.02 [12] Scheffers, G., Anwendung der Differential- und Integralrechnung auf die Geometrie (1902), Leipzig: Veit & Co., Leipzig · JFM 33.0632.08 [13] Schirokow, R. A.; Schirokow, A. R., Affine Differentialgeometrie (1962), Leipzig: Teubner-Verlag, Leipzig · Zbl 0106.14703 [14] Schroder, E., Beitrag zur Krümmungstheorie von regulären Flächen imR_3 unter Einbeziehung eines vollständigen Systems von partiellen Ableitungen bis zur vierten Ordnung, Mitt. Math. Ges. DDR, 4, 77-99 (1977) · Zbl 0388.53002 [15] Su, B., Affine Differential Geometry (1983), Beijing: Science Press, Beijing · Zbl 0539.53002 [16] Transon, A., Recherches sur la courbure des lignes et des surfaces, J. de math. pures et appl., 6, 191-208 (1841) [17] Walker, R. J., Algebraic Curves (1950), Princeton: Princeton University Press, Princeton · Zbl 0039.37701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.