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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Affine surfaces whose geodesics are planar curves


Author: Luc Vrancken
Journal: Proc. Amer. Math. Soc. 123 (1995), 3851-3854
MSC: Primary 53A15; Secondary 53B05
MathSciNet review: 1283565
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Abstract: We study the geometry of nondegenerate affine surfaces $ {M^2}$ in $ {\mathbb{R}^4}$, 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283565-8
PII: S 0002-9939(1995)1283565-8
Keywords: Affine differential geometry, higher codimension, planar geodesies
Article copyright: © Copyright 1995 American Mathematical Society