GEODESICS IN THE TENSOR BUNDLE OF DIAGONAL LIFTS

Abstract

Let $M_n$ be an n-dimensional differentiable manifold of class $C^{\infty}$ and

$T^1_{q}(M_n)$ the tensor bundle over  $M_n$ of tensor of type (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 $T^1_{q}(M_n)$ 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

References

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