2019/02/13 by Gao, Shanze, Ma, Hui
#52A20 #53C40 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1902.04799
We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using a new integral formula or Brendle's Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These results can be viewed as generalizations of the classical Jellet-Liebmann theorem and the Alexandrov theorem in Euclidean space.