Classification theorems of complete space-Like Lagrangian xi-surfaces in the pseudo-Euclidean space R-2(4)
Classification theorems of complete space-Like Lagrangian xi-surfaces in the pseudo-Euclidean space R-2(4)
复制标题
伪欧几里得空间$bbr^4_2$中完全类空间拉格朗日$xi$曲面的分类定理
DOI：
10.1007/s00574-020-00235-4
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Liu Yangyang
中科院分区：
文献类型：
--
作者：
Li Xingxiao;Qiao Ruina;Liu Yangyang
- 子流形和-平移子分别是平均曲率流的自收缩子和平移子的自然推广，在余维为1的情况下，它们以前分别被称为-超曲面和-平移子。本文研究了具有正则复结构的伪欧氏4-空间中的完备Lagrange类空曲面和完备Lagrange类空平移子。作为结果，我们首先得到了第二基本形式的常平方模的完备Lagrange类空曲面的分类定理。然后，证明的主要思想也允许我们获得一个类似的分类定理的-translators在一般的伪欧空间中的类空translators的Bernstein型定理，这是独立的意义。
-submanifolds and-translators are, respectively, the natural generalizations of self-shrinkers and translators of the mean curvature flow and, in the case of codimension one, they are previously known as-hypersurfaces and-translators, respectively. In this paper, we study the complete Lagrangian space-like-surfaces and-translators in, the pseudo-Euclidean 4-spaces of signature 2 endowed with the canonical complex structure. As the result, we first obtain a classification theorem for all complete Lagrangian space-like-surfaces inof constant square norm of the second fundamental form. Then the main idea of the proof also allows us to obtain a similar classification theorem for-translators inby a Bernstein-type theorem for space-like translators in a general pseudo-Euclidean space, which is of independent significance.