On the complete linear Weingarten spacelike hypersurfaces with two distinct principal curvatures in Lorentzian space forms

作者：Gomes Jose N; de Lima Henrique F^*; dos Santos Fabio R; Velasquez Marco Antonio L

来源：Journal of Mathematical Analysis and Applications, 2014, 418(1): 248-263.

DOI：10.1016/j.jmaa.2014.03.090

• Lorentzian space forms
• Mean curvature
• Normalized scalar curvature
• Complete spacelike hypersurfaces
• Isoparametric hypersurfaces

We deal with complete linear Weingarten spacelike hypersurfaces immersed in a Lorentzian space form, having two distinct principal curvatures. In this setting, we show that such a spacelike hypersurface must be isometric to a certain isoparametric hypersurface of the ambient space, under suitable restrictions on the values of the mean curvature and of the norm of the traceless part of its second fundamental form. 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.

• 出版日期2014-10-1