IFP transformations on the cotangent bundle with the modified Riemannian extension

Document Type : Original Article


Department of Mathematical Science and Statistics, Malayer University, Malayer, Iran. Email: m.zohrehvand@malayeru.ac.ir


Let ∇ be a symmetric connection on an n-dimensional manifold M n
and T M n its cotangent bundle. In this paper, firstly, we determine the
infinitesimal fiber-preserving projective(IFP) transformations on T M n
with respect to the Riemannian connection of the modified Riemannian
extension ˜ g ∇,c where c is a symmetric (0,2)-tensor field on M n . Then
we prove that, if (T M n , ˜ g ∇,c ) admits a non-affine infinitesimal fiber-
preserving projective transformation, then M n is locally flat, where ∇
is the Levi-Civita connection of a Riemannian metric g on M n . Finally,
the infinitesimal complete lift, horizontal and vertical lift projective trans-
formations on (T M n , ˜ g ∇,c ) are studied.