Two rigidity results for surfaces in Schwarzschild spacetimes
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 αH = - d |H| studied in 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.
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