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

Mehmet Erdoğan, Jeta Alo

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 Tanaka-Webster connection $\hat{\bigtriangledown}$ is $\xi$-conformally flat. Furthermore, we give some structure theorems on Lorentzian Sasakian manifold with respect to the Tanaka-Webster connection.