Generalized Tanaka-Webster connection on $\beta$-Kenmotsu manifolds

Abstract

This research paper aims to study the postulates of the generalized Tanaka-Webster connection (briefly, gTWc) on $\beta$-Kenmotsu manifolds. We find the curvature properties of a $\beta$-Kenmotsu manifold concerning gTWc, and studied the conditions for the $\phi$-projectively flat, $\phi$-conformally flat and $\phi$-concirculary flat $\beta$-Kenmotsu manifolds along with the same connection. Also, we have discussed the $\xi$-flat properties on same curvatures for the $\beta$-Kenmotsu manifold admitting gTWc. At the end we provide an example to verify some of our results.