Affine surfaces whose geodesics are planar curves
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- by Luc Vrancken
- Proc. Amer. Math. Soc. 123 (1995), 3851-3854
- DOI: https://doi.org/10.1090/S0002-9939-1995-1283565-8
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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.References
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- Wilhelm Klingenberg, Zur affinen Differentialgeometrie. I. Über $p$-dimensionale Minimalflächen und Sphären im $n$-dimensionalen Raum, Math. Z. 54 (1951), 65–80 (German). MR 49637, DOI 10.1007/BF01175136
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- 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