A Connectedness Principle in the Geometry of Positive Curvature
A Connectedness Principle in the Geometry of Positive Curvature
复制标题
DOI：
10.4310/cag.2005.v13.n4.a2
复制
发表时间：
2005
影响因子：
0.7
通讯作者：
F. Fang;S. Mendonça;Xiaochun Rong
中科院分区：
文献类型：
--
作者：
F. Fang;S. Mendonça;Xiaochun Rong
本文的主要目的是发展正曲率几何中的一个连通性原理。在形式上，这是一个令人惊讶的模拟经典连通性原则在复杂的代数几何。将连通性原理应用于全测地浸入，不仅为全测地子流形的经典Synge定理、Frankel定理和Wilking最近的一个定理提供了统一的表述，而且为正曲率几何中的全测地浸入提供了新的连通性定理.然而，连通性原理可能适用于某些不需要存在全测地浸入的情况。
The main purpose of this paper is to develop a connectedness principle in the geometry of positive curvature. In the form, this is a surprising analog of the classical connectedness principle in complex algebraic geometry. The connectedness principle, when applied to totally geodesic immersions, provides not only a uniform formulation for the classical Synge theorem, the Frankel theorem and a recent theorem of Wilking for totally geodesic submanifolds, but also new connectedness theorems for totally geodesic immersions in the geometry of positive curvature. However, the connectedness principle may apply in certain cases which do not require the existence of totally geodesic immersions.