IFP transformations on the cotangent bundle with the modified Riemannian extension

	IFP transformations on the cotangent bundle with the modified Riemannian extension
Journal of Finsler Geometry and its Applications
دوره 1، شماره 2، اسفند 2020، صفحه 27-38 اصل مقاله (95.56 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2020.1237
نویسنده
Mosayeb Zohrehvand^*
Department of Mathematical Science and Statistics, Malayer University, Malayer, Iran. Email: m.zohrehvand@malayeru.ac.ir
چکیده
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.
کلیدواژه‌ها
Modified Riemannian extension؛ Infinitesimal fiber-preserving transformations؛ Infinitesimal projective transformations

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