Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection

Let (M, g) be an n-dimensional (pseudo-)Riemannian manifold and T M be its tangent bundle T M equipped with the complete lift metric Cg. First, we define a Ricci quarter-symmetric metric connection V on the tangent bundle T M equipped with the complete lift metric Cg. Second, we compute all forms of the curvature tensors of V and study their properties. We also define the mean connection of V. Ricci and gradient Ricci solitons are important topics studied extensively lately. Necessary and sufficient conditions for the tangent bundle T M to become a Ricci soliton and a gradient Ricci soliton concerning V are presented. Finally, we search conditions for the tangent bundle T M to be locally conformally flat with respect to V.

Journal

AIMS MATHEMATICS

Year

2023

Volume

8

Issue

8

Pages

17335-17353

eISSN

2473-6988

DOI

10.3934/math.2023886

WoS UID

WOS:000995829700001