On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric

Esmaeil Peyghan, Davood Seifipour and Ion Mihai ()
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Esmaeil Peyghan: Department of Mathematics, Faculty of Science, Arak University, Arak 38156-88349, Iran
Davood Seifipour: Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan 63176-36531, Iran
Ion Mihai: Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania

Mathematics, 2023, vol. 11, issue 18, 1-18

Abstract: In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle T M 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.

Keywords: Codazzi manifold; Kobayashi–Nomizu type connection; mutual curvature; Yano type connection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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