Diagonal Lift in the Cotangent Bundle and its Applications

Authors: SEZGİN AKBULUT, MURAT ÖZDEMİR, ARİF A. SALIMOV

Abstract: The purpose of this paper is to define a diagonal lift ^{\mathcal{D }}g of a Riemannian metric g of a manifold M_{n} to the cotangent bundle T^{*}(M_{n}) of M_{n}, to associate with ^{\mathcal{D}}g an Levi-Civita connection of T^{*}(M_{n}) in a natural way and to investigate applications of the diagonal lifts.

Keywords: Cotangent bundle, Riemannian metric, diagonal lift, Levi-Civita connection, B-manifold, Killing vector field, geodesic.

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