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arXiv · 1809.03639

On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space

A. Borisenko·Y. Nikolayevsky
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Abstract

We consider Finsler submanifolds $M^n$ of nonnegative Ricci curvature in a Minkowski space $\mathbb{M}^{n+p}$ which contain a line or whose relative nullity index is positive. For hypersurfaces, submanifolds of codimension two or of dimension two, we prove that the submanifold is a cylinder, under a certain condition on the inertia of the pencil of the second fundamental forms. We give an example of a surface of positive flag curvature in a three-dimensional Minkowski space which is not locally convex.

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A. Borisenko, Y. Nikolayevsky. 2018-09-10. On cylindricity of submanifolds of nonnegative Ricci curvature in a Minkowski space. https://arxiv.org/abs/1809.03639

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