A note on submanifolds of generalized K\"ahler manifolds
Izu Vaisman
TL;DR
This paper investigates CR-submanifolds within generalized Kähler manifolds, establishing conditions under which the induced structures become CRFK, extending previous results from hypersurfaces.
Contribution
It extends prior work by deriving conditions for CRFK structures on submanifolds of generalized Kähler manifolds, generalizing earlier hypersurface results.
Findings
Conditions for induced generalized F structures to be CRFK
Extension of hypersurface results to submanifolds
Characterization of CR-submanifolds in generalized Kähler manifolds
Abstract
In this note, we consider submanifolds of a generalized K\"ahler manifold that are CR-submanifolds for the two associated Hermitian structures. Then, we establish the conditions for the induced, generalized F structure to be a CRFK structure. The results extend similar conditions which we obtained for hypersurfaces in an earlier paper.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research