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- W4301406932 abstract "We prove the following localized version of a classical ellipsoid characterization: Let $Bsubsetmathbb R^3$ be convex body with a smooth strictly convex boundary and 0 in the interior, and suppose that there is an open set of planes through 0 such that all sections of $B$ by these planes are linearly equivalent. Then all these sections are ellipses and the corresponding part of $B$ is a part of an ellipsoid. We apply this to differential geometry of Finsler surfaces in normed spaces and show that in certain cases the intrinsic metric of a surface imposes restrictions on its extrinsic geometry similar to implications of Gauss' Theorema Egregium. As a corollary we construct 2-dimensional Finsler metrics that do not admit local isometric embeddings to dimension~3." @default.
- W4301406932 created "2022-10-05" @default.
- W4301406932 creator A5088158552 @default.
- W4301406932 date "2017-02-10" @default.
- W4301406932 modified "2023-09-29" @default.
- W4301406932 title "Monochromatic Finsler surfaces and a local ellipsoid characterization" @default.
- W4301406932 doi "https://doi.org/10.48550/arxiv.1702.03340" @default.
- W4301406932 hasPublicationYear "2017" @default.
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