论文标题
HOPF类型定理在Riemannian流形中
Hopf type theorems in Riemannian manifolds
论文作者
论文摘要
1951年，H。Hopf证明了球体的同构表面，在欧几里得空间中具有持续的平均曲率是圆形（几何）球。在本文中，我们调查了Renato Tribuzy的一些贡献，以推广HOPF的结果，以及作者使用这些技术的一些结果来缩小曲率流的孤子和三维翘曲产品歧管中的表面，特别是De de Sitter-SchwarzsChwarzschelds-Schwarzschild和Reissner-Nord-NordStrom scorolds。
In 1951, H. Hopf proved that the only surfaces, homeomorphic to the sphere, with constant mean curvature in the Euclidean space are the round (geometrical) spheres. In this paper we survey some contributions of Renato Tribuzy to generalize the result of Hopf as well as some recent results of the authors using these techniques for shrinking solitons of curvature flows and for surfaces in three-dimensional warped product manifolds, specially the de Sitter-Schwarzschild and Reissner-Nordstrom manifolds.
