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.
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Zohrehvand, M. (2020). IFP transformations on the cotangent bundle with the modified Riemannian extension. Journal of Finsler Geometry and its Applications, 1(2), 27-38. doi: 10.22098/jfga.2020.1237
MLA
Mosayeb Zohrehvand. "IFP transformations on the cotangent bundle with the modified Riemannian extension", Journal of Finsler Geometry and its Applications, 1, 2, 2020, 27-38. doi: 10.22098/jfga.2020.1237
HARVARD
Zohrehvand, M. (2020). 'IFP transformations on the cotangent bundle with the modified Riemannian extension', Journal of Finsler Geometry and its Applications, 1(2), pp. 27-38. doi: 10.22098/jfga.2020.1237
VANCOUVER
Zohrehvand, M. IFP transformations on the cotangent bundle with the modified Riemannian extension. Journal of Finsler Geometry and its Applications, 2020; 1(2): 27-38. doi: 10.22098/jfga.2020.1237
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