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Displaying similar documents to “On the Ricci Tensor of a real hypersurface of quaternionic hyperbolic space.”

Boundaries of Levi-flat hypersurfaces: special hyperbolic points

Pierre Dolbeault (2012)

Annales Polonici Mathematici

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Let S ⊂ ℂⁿ, n ≥ 3, be a compact connected 2-codimensional submanifold having the following property: there exists a Levi-flat hypersurface whose boundary is S, possibly as a current. Our goal is to get examples of such S containing at least one special 1-hyperbolic point: a sphere with two horns, elementary models and their gluings. Some particular cases of S being a graph are also described.

Well posed reduced systems for the Einstein equations

Yvonne Choquet-Bruhat, James York (1997)

Banach Center Publications

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We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.

On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)

Colloquium Mathematicae

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We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.