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Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces

  • Huijuan Wang
  • Hongwei Xu
  • Entao ZhaoEmail author
Article
  • 17 Downloads

Abstract

In the present paper, we prove a rigidity theorem for complete submanifolds with parallel Gaussian mean curvature vector in the Euclidean space \({\mathbb {R}}^{n+p}\) under an integral curvature pinching condition, which is a unified generalization of some rigidity results for self-shrinkers and the \(\lambda \)-hypersurfaces in Euclidean spaces.

Mathematics Subject Classification

53C44 53C42 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center of Mathematical SciencesZhejiang UniversityHangzhouPeople’s Republic of China

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