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Rigidity of linear Weingarten hypersurfaces in locally symmetric manifolds
Author(s) -
Alías Luis J.,
de Lima Henrique F.,
Meléndez Josué,
dos Santos Fábio R.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400296
Subject(s) - hypersurface , mathematics , scalar curvature , principal curvature , rigidity (electromagnetism) , mathematical analysis , mean curvature , curvature , space form , sectional curvature , riemannian manifold , pure mathematics , manifold (fluid mechanics) , geometry , physics , mechanical engineering , quantum mechanics , submanifold , engineering
Our purpose in this paper is to study the rigidity of complete linear Weingarten hypersurfaces immersed in a locally symmetric manifold obeying some standard curvature conditions (in particular, in a Riemannian space with constant sectional curvature). Under appropriated constrains on the scalar curvature function, we prove that such a hypersurface must be either totally umbilical or isometric to an isoparametric hypersurface with two distinct principal curvatures, one of them being simple. Furthermore, we also deal with the parabolicity of these hypersurfaces with respect to a suitable Cheng–Yau modified operator.