半黎曼流形中子流形的几何

A semi-Riemannian manifold, or known as pseudo-Riemannian manifold, is a differentiable manifold equipped with an indefinite metric. One of the real models is the Einstein's space-time in relativity. In particular, Riemannian manifold is a special Semi-Riemannian manifold. The aim of this project is to investigate the geometrical properties of submanifolds in semi-Riemannian manifold (including Riemannian manifold). The emphasis of the project is to study minimal (or maximal) submanifolds, and pay attention to other category of submanifolds such as submanifolds with parallel mean curvature vector, rotating submanifolds, isoparametric hypersurfaces, and so on. Since the period of this project is four years, the project will dedicate to some important open problems of modern differential geometry, and promise to get some progress.

半黎曼流形也叫伪黎曼流形，是带有一个不定度量的微分流形，它的现实模型之一是相对论中的爱因斯坦时空。黎曼流形是特殊的半黎曼流形。本项目的研究目标是半黎曼流形（包括黎曼流形）中子流形的几何性质，重点是其中的极小或极大子流形，同时对别的类型的子流形如平行平均曲率子流形、旋转型子流形、等参超曲面等也予以关注。因为研究期限为四年，本项目将对当代微分几何中几个重要的未解决问题开展研究，期望能获得突破。

半黎曼流形也叫伪黎曼流形，是带有一个不定度量的微分流形，它的现实模型之一是相对论中的爱因斯坦时空。黎曼流形是特殊的半黎曼流形。本项目的研究目标是半黎曼流形（包括黎曼流形）中子流形的几何性质，重点是其中的极小或极大子流形，同时对别的类型的子流形如平行平均曲率子流形、旋转型子流形、等参超曲面等也予以关注。本项目圆满解决了洛伦兹球面$S^{n+1}_1$中的Lorentz等参超曲面的分类问题。对3维拓扑球面$S^3$到复射影空间$CP^n$中的等变CR极小浸入取得了重大进展。