On hypersurfaces of generalized Kähler manifolds

Abstract

We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized Kähler 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 Kähler, the structure on $M$ is said to be binormal. We characterize binormality and give an example of binormal structure.

LaTeX, 30 pages. References and corresponding comments added

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• Modular Classes of Loday Algebroids
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Cited by in corpus (1)

• A note on submanifolds of generalized Kähler manifolds