The Rigidity Theorems of Self Shrinkers via Gauss maps

Details The Rigidity Theorems of Self Shrinkers via Gauss maps The Rigidity Theorems of Self Shrinkers via Gauss maps

2012-03-06

arxiv.org/abs/1203.1096v1

Mathematics

Differential Geometry

22 pages

Scientific paper

We study the rigidity results for self-shrinkers in Euclidean space by restriction of the image under the Gauss map. The geometric properties of the target manifolds carry into effect. In the self-shrinking hypersurface situation Theorem 3.1 and Theorem 3.2 not only improve the previous results, but also are optimal. In higher codimensional case, using geometric properties of the Grassmanian manifolds (the target manifolds of the Gauss map) we give a rigidity theorem for self-shrinking graphs.

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