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Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces

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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.

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Authors and Affiliations

  1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Huijuan Wang, Hongwei Xu & Entao Zhao

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  1. Huijuan Wang
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  2. Hongwei Xu
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  3. Entao Zhao
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Correspondence to Entao Zhao.

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Research supported by the National Natural Science Foundation of China, Grant Nos. 11531012, 11371315, 11201416.

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Wang, H., Xu, H. & Zhao, E. Submanifolds with parallel Gaussian mean curvature vector in Euclidean spaces. manuscripta math. 161, 439–465 (2020). https://doi.org/10.1007/s00229-019-01104-1

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