Two rigidity results for surfaces in Schwarzschild spacetimes

Po-Ning Chen; Ye-Kai Wang

Two rigidity results for surfaces in Schwarzschild spacetimes

Differential Geometry 2023-06-14 v1

Authors: Po-Ning Chen , Ye-Kai Wang

Abstract

We prove two rigidity results for surfaces lying in the standard null hypersurfaces of Schwarzschild spacetime satisfying certain mean curvature type equations. The first is for the equation $\alpha_H = - d\log |H|$ studied in \cite{WWZ}. The second is for the mean curvature vector of constant norm. The latter is related to the Liouville and Obata Theorem in conformal geometry.

Keywords

surfaces with constant mean curvature hypersurfaces general relativity

Cite

@article{arxiv.2306.07477,
  title  = {Two rigidity results for surfaces in Schwarzschild spacetimes},
  author = {Po-Ning Chen and Ye-Kai Wang},
  journal= {arXiv preprint arXiv:2306.07477},
  year   = {2023}
}

Comments

22 pages, 1 figure

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