On hypersurfaces of generalized K\"ahler manifolds

Izu Vaisman

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arXiv · 1705.10073

On hypersurfaces of generalized K\"ahler manifolds

Izu Vaisman

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Abstract

We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized K\"ahler manifold to be a generalized CRFK structure. Then, we discuss a notion of generalized almost contact structure on a manifold $M$ that is suggested by the induced structure of a hypersurface. Such a structure has an associated generalized almost complex structure on $M\times\mathds{R}$. If the latter is integrable, the former is normal and we give the corresponding characterization. If the structure on $M\times\mathds{R}$ is generalized K\"ahler, the structure on $M$ is said to be binormal. We characterize binormality and give an example of binormal structure.

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Izu Vaisman. 2017-05-29. On hypersurfaces of generalized K\"ahler manifolds. https://arxiv.org/abs/1705.10073

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