On xi-Conformally and xi-Pseudo Projectively Flat Lorentzian Sasakian Manifolds with Tanaka-Webster Connection

Abstract

In this work, the Tanaka-Webster connection on a Lorentzian Sasakian manifold is defined and the notions xi-quasi conformally and xi-pseudo projectively flat structures on a Lorentzian Sasakian manifold are introduced. After that, it is proved that if any Lorentzian Sasakian manifold with Tanaka-Webster connection is an eta- Einstein manifold, then the Thnaka-Webster connection (del) over cap is xi-conformally flat. Furthermore, we give some structure theorems on Lorentzian Sasakian manifold with respect to the Tanaka-Webster connection.