Diagonal Lift in the Tangent Bundle of Order Two and its Applications

Authors: FOUZI HATHOUT, H. M. DIDA

Abstract: In this paper we define a diagonal lift ^{D}g of Riemannian metric g of manifold M_n to the tangent bundle of order two denoted by T^{2}M_n of M_n, we associate to ^{D}g its Levi-civita connection of T^2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.

Keywords: Tangent bundle of order two, Riemannian metric, Diagonal lift, Levi-civita connection, Killing vector field, Geodesic

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