Pseudo-Sasakian manifolds endowed with a contact conformal connection

Abstract

Pseudo-Sasakian manifolds M˜(U,ξ,η˜,g˜) endowed with a contact conformal connection are defined. It is proved that such manifolds are space forms M˜(K), K<0, and some remarkable properties of the Lie algebra of infinitesimal transformations of the principal vector field U˜ on M˜ are discussed. Properties of the leaves of a co-isotropic foliation on M˜ and properties of the tangent bundle manifold TM˜ having M˜ as a basis are studied.