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

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran

2 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

3 Department of Pure Mathematics, Calcutta University, 35, B.C.Road, Kolkata-700019, India



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.


Articles in Press, Corrected Proof
Available Online from 05 April 2023
  • Receive Date: 19 November 2022
  • Revise Date: 13 February 2023
  • Accept Date: 30 March 2023
  • First Publish Date: 05 April 2023