GEODESICS IN THE TENSOR BUNDLE OF DIAGONAL LIFTS

Authors : N. CENGİZ, A. A. SALİMOV

Pages : 1-11

View : 15 | Download : 5

Publication Date : 2001-12-01

Article Type : Research Paper

Abstract :Let $M_n$ be an n-dimensional differentiable manifold of class $C^{\infty}$ and $T^1_{q}insert ignore into journalissuearticles values(M_n);$ the tensor bundle over  $M_n$ of tensor of type insert ignore into journalissuearticles values(1,q);. The purpose of this paper is to de¯ne a diagonal lift $^D_g$ of a Riemannian metric g of a  manifold $M_n$ to the tensor bundle $T^1_{q}insert ignore into journalissuearticles values(M_n);$  and and to investigate  geodesics in a tensor bundle with respect to the Levi-Civita connection of  $^D_g$.
Keywords : Tensor bundle, Riemannian metric, Diagonal lift, Levi Civita connection, Geodesic