Displaying similar documents to “On complete spacelike hypersurfaces with R = a H + b in locally symmetric Lorentz spaces”

Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces

Yaning Wang, Ximin Liu (2012)

Archivum Mathematicum

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A new class of ( n + 1 ) -dimensional Lorentz spaces of index 1 is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.

A new characterization of r -stable hypersurfaces in space forms

H. F. de Lima, M. A. Velásquez (2011)

Archivum Mathematicum

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In this paper we study the r -stability of closed hypersurfaces with constant r -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the r -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the r -th mean curvature.