Generalized almost contact structures and generalized Sasakian structures

Abstract

We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide the notion of generalized Sasakian structures from the view point of the generalized almost contact structures. We obtain a generalized Sasakian structure on a non-compact manifold which does not arise as a pair of ordinary Sasakian structures. However we show that a generalized Sasakian structure on a compact $3$-dimensional manifold is equivalent to a pair of Sasakian structures with the same metric.