Affine surfaces whose geodesics are planar curves

Vrancken, Luc

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

Affine surfaces whose geodesics are planar curves
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Proc. Amer. Math. Soc. 123 (1995), 3851-3854 Request permission

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.

References

Die Geometrie zweifach ausgedehnter Mannigfaltigkeiten

im affinen Raum

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