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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 | ||
آمار تعداد مشاهده مقاله: 136 تعداد دریافت فایل اصل مقاله: 129 |