Abstract

The present paper aims to define and discuss $ (\mathcal{L}cs)_{n} $-manifolds and Schouten van Kampen connection. We discussed the curvature tensor and Ricci curvature tensor of this manifold with respect to the $\mathcal{SVK}$-connection. We studied conformally flat, projectively flat, conharmonically flat, and concircularly flat $(\mathcal{L}cs)_{n}$-manifolds with the $\mathcal{SVK}$-connection. At last, we gave an example of $ (\mathcal{L}cs)_{n} $-manifolds with $\mathcal{SVK}$-connection.

Keywords and Phrases

$(\mathcal{L}cs)_{n}$-manifold, $\mathcal{SVK}$-connection.

A.M.S. subject classification

53C15, 53C20.

.....