A rigidity theorem of $\xi$-submanifolds in $\mathbb{C}^{2}$

Xingxiao Li; Xiufen Chang

A rigidity theorem of $\xi$-submanifolds in $\mathbb{C}^{2}$

Differential Geometry 2015-11-10 v1

Authors: Xingxiao Li , Xiufen Chang

Abstract

In this paper, we first introduce the concept of $\xi$ -submanifold which is a natural generalization of self-shrinkers for the mean curvature flow and also an extension of $\lambda$ -hypersurfaces to the higher codimension. Then, as the main result, we prove a rigidity theorem for Lagrangian $\xi$ -submanifold in the complex $2$ -plane $\bbc^2$ .

Keywords

xi-submanifold self-shrinker mean curvature flow lambda-hypersurface Lagrangian submanifold rigidity theorem

Cite

@article{arxiv.1511.02568,
  title  = {A rigidity theorem of $\xi$-submanifolds in $\mathbb{C}^{2}$},
  author = {Xingxiao Li and Xiufen Chang},
  journal= {arXiv preprint arXiv:1511.02568},
  year   = {2015}
}

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