On Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi-$ connection

Ajit Barman ; Uday Chand De ; Pradip Majhi 

Novi Sad Journal of Mathematics, Tome 48 (2018) no. 1.

Résumé

The object of the present paper is to study a special type of semi-symmetric non-metric $\phi$-connection on a Kenmotsu manifold. It is shown that if the curvature tensor of Kenmotsu manifolds admitting a special type of semi-symmetric non-metric $\phi$-connection $\bar{\nabla}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^n(-1)$. Beside these, we consider Weyl conformal curvature tensor of a Kenmotsu manifold with respect to the semi-symmetric non-metric $\phi$-connection. Among other results, we prove that the Weyl conformal curvature tensor with respect to the Levi-Civita connection and the semi-symmetric non-metric $\phi$-connection are equivalent. Moreover, we deal with $\phi$-Weyl semi-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric $\phi$-connection. Finally, an illustrative example is given to verify our result.

Détail

Publié le : 2018-02-14

DOI : 10.30755/NSJOM.06311

Classification : 53C15, 53C25
Keywords: Kenmotsu manifold, semi-symmetric non-metric $\phi$-connection, Weyl conformal curvature tensor, $\phi$-Weyl semi-symmetric, Levi-Civita connection