论文标题
HOPF类型定理用于De Sitter-Schwarzschild和Reissner-Nordstrom歧管
Hopf type theorems for surfaces in the de Sitter-Schwarzschild and Reissner-Nordstrom 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。这些结果由S. S. Chern，然后由Eschenburg和Tribuzy概括为表面，在带有恒定截面曲率的Riemannian歧管中，对球体的同构表面，其平均曲率功能满足其差异的某些结合。 In this paper, using techniques partial differential equations in the complex plane which generalizes the notion of holomorphy, we extend these results for surfaces in a wide class of warped product manifolds, which includes, besides the classical space forms of constant sectional curvature, the de Sitter-Schwarzschild manifolds and the Reissner-Nordstrom manifolds, which are time slices of solutions of the Einstein field equations of the general相对论。
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. These results were generalized by S. S. Chern, and then by Eschenburg and Tribuzy, for surfaces, homeomorphic to the sphere, in Riemannian manifolds with constant sectional curvature whose mean curvature function satisfies some bound on its differential. In this paper, using techniques partial differential equations in the complex plane which generalizes the notion of holomorphy, we extend these results for surfaces in a wide class of warped product manifolds, which includes, besides the classical space forms of constant sectional curvature, the de Sitter-Schwarzschild manifolds and the Reissner-Nordstrom manifolds, which are time slices of solutions of the Einstein field equations of the general relativity.
