Kenmotsu manifolds endowed with the semi-symmetric non-metriC $\phi$-connection to its tangent bundle

Uday Chand De ; Mohammad Nazrul Islam Khan 

Novi Sad Journal of Mathematics, Tome 54 (2024) no. 1.

Résumé

The goal of this paper is to study the complete lift of the semi-symmetric non-metric $\phi$-connection on a Kenmotsu manifold to its tangent bundle $TM$ and to obtain a relation between the semi-symmetric non-metric $\phi$-connection $\bar{D}^C$ on Kenmotsu manifolds with respect to Levi-Civita connection $D^C$ by utilizes specialized mathematical operators. on $TM$. Next, the complete lifts of the curvature tensor, the scalar curvature and the Ricci tensor on $TM$ are constructed and show that Ricci tensor is symmetric on $TM$. Finally, a study of the complete lift of curvature tensor concerning the semi-symmetric non-metric $\phi$-connection to its tangent bundle $TM$ is done which shows that if the complete lift of the curvature tensor of $\bar{D}^C$ vanishes on $TM$, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^n(1)$ on $TM$.

Détail

Publié le : 2022-03-15

DOI : 10.30755/NSJOM.13758

Classification : 53C05, 53C25, 58A30
Keywords: complete lift, tangent bundle, Kenmotsu manifold, semi-symmetric non-metric $\phi$-connection, curvature tensor, mathematical operators, scalar Ricci tensorr