On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric - Esmaeil Peyghan; Davood Seifipour; Ion Mihai (Mathematics, 2023)
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle <semantics>TM</semantics> equipped with the Sasaki metric. Then, we determine the curvature tensors of these connections. Moreover, we find conditions under which these connections are torsion-free, Codazzi, and statistical structures, respectively, with respect to the Sasaki metric. Finally, we introduce the mutual curvature tensor on a manifold. We investigate some of its properties; furthermore, we study mutual curvature tensors on a manifold equipped with the Kobayashi–Nomizu type and the Yano type connections.