Partial generalizations of some Conjectures in locally symmetric Lorentz spaces

2013/09/07 by Zhongyang Sun, Sun, Zhongyang
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1309.1840

arxiv created 2013/09/07 · arxiv updated 2013/09/10

Abstract

In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P+aH=b in a locally symmetric Lorentz space L₁ⁿ⁺¹. Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces L₁ⁿ⁺¹ satisfying some curvature conditions. By modifying Cheng-Yau's operator \square given in \citeChengYau77, we introduce a modified operator L and give new estimates of L(nH) and \square(nH) of such spacelike hypersurfaces. Finally, we give partial generalizations of some conjectures in locally symmetric Lorentz spaces L₁ⁿ⁺¹.

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