University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 1 2 2020 12 01 IFP transformations on the cotangent bundle with the modified Riemannian extension 27 38 1237 10.22098/jfga.2020.1237 EN Mosayeb Zohrehvand Department of Mathematical Science and Statistics, Malayer University, Malayer, Iran. Email: m.zohrehvand@malayeru.ac.ir Journal Article 2021 01 01 Let ∇ be a symmetric connection on an n-dimensional manifold M _n<br />and T ^∗ M n its cotangent bundle. In this paper, firstly, we determine the<br />infinitesimal fiber-preserving projective(IFP) transformations on T ^∗ M _n<br />with respect to the Riemannian connection of the modified Riemannian<br />extension ^˜ g ∇_,c where c is a symmetric (0,2)-tensor field on M_n . Then<br />we prove that, if (T ^∗ M _n , ^˜ g ∇_,c ) admits a non-affine infinitesimal fiber-<br />preserving projective transformation, then M n is locally flat, where ∇<br />is the Levi-Civita connection of a Riemannian metric g on M _n . Finally,<br />the infinitesimal complete lift, horizontal and vertical lift projective trans-<br />formations on (T ^∗ M _n ,^˜ g ∇_,c ) are studied. https://jfga.uma.ac.ir/article_1237_72b2d06af7c5c765d2445eff11c74e51.pdf