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

Authors: ESMAEIL PEYGHAN, DAVOOD SEIFIPOUR, ADARA BLAGA

Abstract: 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.

Keywords: Codazzi manifold, lift connections, lift metrics, Osserman structure, statistical manifold

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