How many statistical structures and Ricci flat affine connections are there on the tangent bundle?

	How many statistical structures and Ricci flat affine connections are there on the tangent bundle?
International Journal of Nonlinear Analysis and Applications
مقاله 19، دوره 15، شماره 1، فروردین 2024، صفحه 225-239 اصل مقاله (452.46 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29053.4052
نویسندگان
Esmaeil Peyghan^* ¹؛ Farshad Firuzi²؛ Uday Chand De³
¹Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran
²Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran
³Department of Pure Mathematics, Calcutta University, 35, B.C.Road, Kolkata-700019, India
چکیده
In this paper, we consider the tangent bundle TM of a Riemannian manifold (M, g) with the Sasaki metric G and using the Cauchy-Kowalevski Theorem, we answer the question of how many analytic statistical structures are there on (TM, G). Also, we study the Ricci tensor of linear affine connections on the tangent bundle TM. In addition, we answer the question of how many Ricci flat affine connections with and without torsion are there on the tangent bundle.
کلیدواژه‌ها
Cauchy-Kowalevski Theorem؛ Sasaki Metrics؛ Statistical Structures
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