Foliations by Spacelike Hypersurfaces on Lorentz Manifolds
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DOI: 10.1007/s00025-020-1159-8
Abstract: In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and applies it to investigate conditions… read more here.
Keywords: lorentz manifolds; foliations spacelike; hypersurfaces lorentz; spacelike hypersurfaces ... See more keywords
f-stability of spacelike hypersurfaces in weighted spacetimes
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DOI: 10.1007/s10474-017-0731-5
Abstract: We establish the notions of f-stability and strong f-stability concerning closed spacelike hypersurfaces immersed with constant f-mean curvature in a conformally stationary spacetime endowed with a conformal timelike vector field V and a weight function… read more here.
Keywords: hypersurfaces weighted; closed spacelike; stability; spacelike hypersurfaces ... See more keywords
Complete spacelike hypersurfaces in orthogonally splitted spacetimes
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DOI: 10.1007/s10714-017-2294-8
Abstract: We provide some “half-space theorems” for spacelike complete non-compact hypersurfaces into orthogonally splitted spacetimes. In particular we generalize some recent work of Rubio and Salamanca on maximal spacelike compact hypersurfaces. Beside compactness, we also relax… read more here.
Keywords: complete spacelike; splitted spacetimes; hypersurfaces orthogonally; orthogonally splitted ... See more keywords
Complete spacelike hypersurfaces on symmetric spacetimes
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DOI: 10.1088/1361-6382/ab6f81
Abstract: A Lorentz manifold is said to be a conformally stationary spacetime if it is endowed with a globally defined conformal timelike vector field K, whereas it is a pp-wave when there is a globally defined… read more here.
Keywords: complete spacelike; symmetric spacetimes; vector field; spacelike hypersurfaces ... See more keywords
Bernstein type results for complete spacelike hypersurfaces immersed in a weighted conformally stationary spacetime
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DOI: 10.1142/s0129167x17500719
Abstract: In this paper, we deal with complete noncompact spacelike hypersurfaces immersed in a weighted conformally stationary spacetime endowed with a closed conformal timelike vector field V. Under suitab... read more here.
Keywords: stationary spacetime; conformally stationary; immersed weighted; hypersurfaces immersed ... See more keywords