Generic Submersions in Contact Geometry

Abstract

In the present paper, we introduce a new type of Riemannian submersion in the contact framework such that the fibers of such submersion are generic submanifolds, as given in [10]. This type of submersion is a generalization of many kinds of submersion introduced before in the literature. Once the Reeb vector field \xi is tangent to the fibers, its position is given such that it should lie in the anti-invariant distribution D^0, which is given in the definition of the generic submersion. Moreover, we give an example and some results for such submersions.