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

2021/12/14 by Peyghan, Esmaeil, Seifipour, Davood, Blaga, Adara M.
#53B20 #53C05 #53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.07202

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.

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