CR structures, k-contact structures, and generalized Sasakian structures

TL;DR

This paper explores the relationship between generalized Sasakian structures and classical geometric structures, establishing equivalences and conditions under which CR and k-contact manifolds are generalized Sasakian.

Contribution

It proves that k-contact manifolds are generalized Sasakian if and only if they are classical Sasakian, and shows that strictly pseudo-convex CR manifolds are always generalized Sasakian.

Findings

k-contact manifolds are generalized Sasakian iff they are classical Sasakian

Strictly pseudo-convex CR manifolds are always generalized Sasakian

Provides new insights into the structure of generalized contact geometry

Abstract

In previous work (arXiv:2205.12067), we defined a notion of a generalized Sasakian structure in the context of generalized contact geometry, the odd dimensional analogue of generalized complex geometry introduced by Hitchin and Gualtieri. We show here that k-contact manifolds are generalized Sasakian if and only if they are classically Sasakian. We show also that strictly pseudo-convex CR manifolds are always generalized Sasakian.