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On the embedding of 1-convex manifolds with 1-dimensional exceptional set

Lucia Alessandrini, Giovanni Bassanelli (2001)

Annales de l’institut Fourier

In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold X , with 1- dimensional exceptional set S and finitely generated second homology group H 2 ( X , ) , is embeddable in m × n if and only if X is Kähler, and this case occurs only when S does not contain any effective curve which is a boundary.

On the Example of Almost Pseudo-Z-symmetric Manifolds

Kanak Kanti Baishya, Patrik Peška (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the present paper we have obtained a new example of non-Ricci-flat almost pseudo-Z-symmetric manifolds in the class of equidistant spaces, which admit non-trivial geodesic mappings.

On the first eigenvalue of spacelike hypersurfaces in Lorentzian space

Bing Ye Wu (2006)

Archivum Mathematicum

In this paper we obtain a lower bound for the first Dirichlet eigenvalue of complete spacelike hypersurfaces in Lorentzian space in terms of mean curvature and the square length of the second fundamental form. This estimate is sharp for totally umbilical hyperbolic spaces in Lorentzian space. We also get a sufficient condition for spacelike hypersurface to have zero first eigenvalue.

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