On hypersurfaces of generalized K\"ahler manifolds

TL;DR

This paper explores the geometric structures induced on hypersurfaces within generalized Kähler manifolds, establishing conditions for various generalized structures and introducing a new notion of generalized almost contact structures.

Contribution

It provides new conditions for hypersurfaces to have generalized CRFK structures and introduces a generalized almost contact structure with a characterization of binormality.

Findings

Conditions for hypersurfaces to be generalized CRFK

Definition and properties of generalized almost contact structures

Characterization of binormal structures

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.