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First Natural Connection on Riemannian Π-Manifolds

Author

Listed:
  • Hristo Manev

    (Department of Medical Physics and Biophysics, Faculty of Pharmacy, Medical University of Plovdiv, 15A Vasil Aprilov Blvd., 4002 Plovdiv, Bulgaria)

Abstract

A natural connection with torsion is defined, and it is called the first natural connection on the Riemannian Π-manifold. Relations between the introduced connection and the Levi–Civita connection are obtained. Additionally, relations between their respective curvature tensors, torsion tensors, Ricci tensors, and scalar curvatures in the main classes of a classification of Riemannian Π-manifolds are presented. An explicit example of dimension five is provided.

Suggested Citation

  • Hristo Manev, 2023. "First Natural Connection on Riemannian Π-Manifolds," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1146-:d:1080326
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