@article{Li2023, 
author = {Yanlin Li and Aydin Gezer and Erkan Karakaş},
title = {Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {17335-17353},
keywords = {Ricci soliton, vector field, tangent bundle, complete lift metric, Ricci quarter-symmetric metric connection},
url = {https://www.sciopen.com/article/10.3934/math.2023886},
doi = {10.3934/math.2023886},
abstract = {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                  C        g. First, we define a Ricci quarter-symmetric metric connection        ∇    ¯   on the tangent bundle    T  M equipped with the complete lift metric                  C        g. Second, we compute all forms of the curvature tensors of        ∇    ¯   and study their properties. We also define the mean connection of        ∇    ¯  . 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        ∇    ¯   are presented. Finally, we search conditions for the tangent bundle    T  M to be locally conformally flat with respect to        ∇    ¯  .}
}