Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space

Year, pages: 2019, 1437 - 1446

Our purpose in this paper is to study complete linear Weingarten space-like hypersurface immersed in locally symmetric Lorentz space obeying some curvature conditions. Our approach is based on the use of a Simons type formula related to an appropriated Cheng-Yau modified operator jointly with some generalized maximum principles, we obtain that such a space-like hypersurface must be either totally umbilical or isometric to an isoparametric hypersurface with two distinct principal curvatures, one of which is simple. This result corresponds to a natural improvement of previous ones due to de Lima, dos Santos, Velásquez [\textit{On the umbilicity of complete linear Weingarten spacelike hypersurfaces immersed in a locally symmetric Lorentz space}, S {a}o Paulo J. Math. Sci. \textbf{11} (2017), 456–470] and Al\'{i}as, de Lima, dos Santos [\textit{New characterizations of linear Weingarten spacelike hypersurfaces in de Sitter space}, Pacific J. Math. \textbf{292} (2018), 1–19].

Mi, R. 2019. Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space. In Mathematica Slovaca, vol. 69, no.6, pp. 1437-1446. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0320

Mi, R. (2019). Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space. Mathematica Slovaca, 69(6), 1437-1446. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0320

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava