Impact of Schouten-van Kampen Connection on LP-Sasakian Manifolds

Abstract

In this paper, we explore the geometric structure of LP-Sasakian manifolds in the context of the Schouten-van Kampen connection. We investigate the interplay between this connection and various curvature-related properties of the manifold. It is established that an LP-Sasakian manifold is locally $\phi$-symmetric with respect to the Schouten-van Kampen connection if and only if the same holds for the Levi-Civita connection. Furthermore, we demonstrate that if an LP-Sasakian manifold is $\phi$-recurrent under the Schouten-van Kampen connection, then it necessarily satisfies the $\eta$-Einstein condition with respect to the Levi-Civita connection. We also prove that quasi-conharmonically flat, conharmonically flat and  $\phi$-conharmonically flat LP-Sasakian manifolds admitting the Schouten-van Kampen connection are likewise $\eta$-Einstein manifolds.