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

JOURNAL OF GEOMETRY AND PHYSICS

卷:155

Article

Borisenko, A.¹  Nikolayevsky, Y.² 

[1] Natl Acad Sci Ukraine, B Verkin Inst Low Temp Phys & Engn, Dept Differential Equat & Geometry, UA-61103 Kharkiv, Ukraine

[2] La Trobe Univ, Dept Math & Stat, Melbourne, Vic 3086, Australia

关键词: Finsler submanifold;    Ricci curvature;    Cylindricity;    Nullity index;    Flag curvature;   

DOI  :  10.1016/j.geomphys.2020.103776

来源: Elsevier

【 摘 要 】

We consider Finsler submanifolds of nonnegative Ricci curvature in a Minkowski space 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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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