On the geometry of lift metrics and lift connections on the tangent bundle

Esmaeil Peyghan, Davood Seifipour, Adara M. Blaga

Published 2021-12-14, updated 2022-03-09Version 2

We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection.