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

Author

Listed:
  • Esmaeil Peyghan

    (Department of Mathematics, Faculty of Science, Arak University, Arak 38156-88349, Iran
    These authors contributed equally to this work.)

  • Davood Seifipour

    (Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan 63176-36531, Iran
    These authors contributed equally to this work.)

  • Ion Mihai

    (Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania)

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.

Suggested Citation

  • Esmaeil Peyghan & Davood Seifipour & Ion Mihai, 2023. "On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3865-:d:1236791
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    References listed on IDEAS

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    1. Yanlin Li & Sujit Bhattacharyya & Shahroud Azami & Apurba Saha & Shyamal Kumar Hui, 2023. "Harnack Estimation for Nonlinear, Weighted, Heat-Type Equation along Geometric Flow and Applications," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Stéphane Puechmorel, 2020. "Lifting Dual Connections with the Riemann Extension," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
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