Mohammad Nazrul Islam Khan

The main aim of the proposed paper is to investigate the lifts of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We investigate several properties of the lifts of the curvature tensor, the conformal curvature tensor, and the conharmonic curvature tensor of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We also study and discover that the lift of the Kenmotsu manifold that admit NSNMC is regular in the tangent bundle. Additionally, we find that the data provided by the lift of Ricci soliton on the lift of Ricci semi-symmetric Kenmotsu manifold that admits NSNMC in the tangent bundle are expanding.

In this work, we have characterized the frame bundle FM admitting metallic structures on almost quadratic ϕ-manifolds ϕ2=pϕ+qI−qη⊗ζ, where p is an arbitrary constant and q is a nonzero constant. The complete lifts of an almost quadratic ϕ-structure to the metallic structure on FM are constructed. We also prove the existence of a metallic structure on FM with the aid of the J˜ tensor field, which we define. Results for the 2-Form and its derivative are then obtained. Additionally, we derive the expressions of the Nijenhuis tensor of a tensor field J˜ on FM. Finally, we construct an example of it to finish.

The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle TM. Certain results on a semisymmetric P-Sasakian manifold, generalized recurrent P-Sasakian manifolds, and pseudo-symmetric P-Sasakian manifolds on TM are proved.