A Note on a Well-Defined Sectional Curvature of a Semi-Symmetric Non-Metric Connection

Author:

Mihai Adela1ORCID,Mihai Ion2ORCID

Affiliation:

1. Transilvania University of Brasov

2. University of Bucharest

Abstract

In this note we propose a new sectional curvature on a Riemannian manifold endowed with a semi-symmetric non-metric connection. A Chen-Ricci inequality is proven. Some possible applications in other fields are mentioned.

Funder

Ministry of Research, Innovation and Digitization, CNCS-UEFISCDI

Publisher

International Electronic Journal of Geometry, Person (Kazim ILARSLAN)

Reference13 articles.

1. [1] Agashe, N.S.: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. Pure Appl. Math. 23, 399–409 (1992).

2. [2] Agashe, N.S.; Chafle, M.R.: On submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection. Tensor 55, 120–130 (1994).

3. [3] Chen, B.-Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimentions. Glasgow Math. J. 41, 33–41 (1999).

4. [4] Cimpoesu, F.; Mihai, A.: Characterizing the E ⊗ e Jahn-Teller potential energy surfaces by differential geometry tools, Symmetry 14(3), art 436 (2022).

5. [5] Friedmann, A.; Schouten, J.A.: Über die Geometrie der halbsymmetrischen Übertragungen. Math. Z. 21, 211–223 (1924).

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1. Constant sectional curvature surfaces with a semi-symmetric non-metric connection;Journal of Mathematical Analysis and Applications;2025-02

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