Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold

Abstract

It is proved that any co-isotropic submanifold M of a pseudo-Sasakian manifold M˜(U,ξ,η˜,g˜) is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distribution ν1. The leaves M1 of D1 are isotropic and M is ν1-totally geodesic. If M is foliate, then M is almost minimal. If M is Ricci D1-exterior recurrent, then M receives two contact Lagrangian foliations. The necessary and sufficient conditions for M to be totally minimal is that M be contact D1-exterior recurrent.