Affine surfaces whose geodesics are planar curves
Author:
Luc Vrancken
Journal:
Proc. Amer. Math. Soc. 123 (1995), 3851-3854
MSC:
Primary 53A15; Secondary 53B05
DOI:
https://doi.org/10.1090/S0002-9939-1995-1283565-8
MathSciNet review:
1283565
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Abstract | References | Similar Articles | Additional Information
Abstract: We study the geometry of nondegenerate affine surfaces in
, with respect to the Burstin-Mayer, the Weise-Klingenberg and the equiaffine transversal plane bundle. A classification is obtained of the surfaces whose geodesies with respect to the induced connection are planar curves.
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im affinen Raum
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F. Dillen, G. Mys, L. Verstraelen, and L. Vrancken, The affine mean curvature vector for surfaces in
, Math. Nachr. 166 (1994), 155-165. MR 1273330 (95b:53013)
- [K] W. Klingenberg, Zur affinen Differentialgeometrie, Teil I: Uber p-dimensionale Minimal-flächen und Sphären im n-dimensionalen Raum, Math. Z. 54 (1951), 65-80. MR 0049637 (14:206b)
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K. Nomizu and L. Vrancken, A new equiaffine theory for surfaces in
, Internat. J. Math. 4 (1993), 127-165. MR 1209963 (94f:53014)
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C. Scharlach and L. Vrancken, Affine transversal planes for surfaces in
, Geometry and Topology of Submanifolds V, World Scientific, Singapore, 1993, pp. 249-253. MR 1339979 (96k:53009)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1995-1283565-8
Keywords:
Affine differential geometry,
higher codimension,
planar geodesies
Article copyright:
© Copyright 1995
American Mathematical Society