Lorentzian $\beta$-Kenmotsu manifold admitting generalized Tanaka-Webster connection

Abstract

In this manuscript, we investigate Lorentzian $\beta$-Kenmotsu manifold admitting generalized Tanaka-Webster connection (GTWC) $\widetilde{\nabla}$. We study curvature tensor and its properties with respect to the above connection. Further, we study the connection on extended generalized $\varphi$-recurrent Lorentzian $\beta$-Kenmotsu manifold. We also investigate the properties of projectively flat, $\zeta$-projectively flat and $\eta$-parallel $\varphi$-tensor on Lorentzian $\beta$-Kenmotsu manifold admitting the connection $\widetilde{\nabla}$. Moreover, we study Ricci soliton on the above manifold with respect to the connection (GTWC). Finally, we give an example of $3$-dimensional Lorentzian $\beta$-Kenmotsu manifold verifying our results.