Affine surfaces whose geodesics are planar curves

Vrancken, Luc

doi:10.1090/S0002-9939-1995-1283565-8

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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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