Abstract

In this article, we examine para - Kenmotsu manifolds equipped with a quarter-symmetric metric connection, focusing on various geometric and curvature properties and we construct an example of a 3-dimensional para-Kenmotsu manifold which confirms the specified metric and structure fulfill the para-Kenmotsu curvature conditions. A unique relation between the curvature tensors of Para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and the Levi-Civita connection has been established. We explore the characteristics of the locally $\phi$-symmetric para-Kenmotsu manifold with respect to the quarter-symmetric metric connection and show that a para-Kenmotsu manifold admitting the quarter-symmetric metric connection $\tilde \nabla$ is locally $\phi$-symmetric if and only if it is so with respect to the Levi-Civita connection. In addition, we studied $\phi$-recurrent para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and proved that if a para-Kenmotsu manifold is $\phi$-recurrent with respect to the quarter-symmetric metric connection, then the manifold is an $\eta$-Einstein manifold with respect to the Levi-Civita connection

Keywords and Phrases

Para-Kenmotsu manifolds, quarter-symmetric metric connection, $\phi$-recurrent para-Kenmotsu manifolds, $\phi$-symmetric para-Kenmotsu manifolds, Einstein manifold.

A.M.S. subject classification

53C25, 53C15.

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