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

Xingxiao Li; Xiufen Chang

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arXiv · 1511.02568

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

Xingxiao Li·Xiufen Chang

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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 $\bbc^2$.

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BibTeX RIS

Xingxiao Li, Xiufen Chang. 2015-11-09. A rigidity theorem of $\xi$-submanifolds in $\mathbb{C}^{2}$. https://arxiv.org/abs/1511.02568

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