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.
Keywords
Linear connection semi-symmetric connection metric connection non-metric connection sectional curvature
Supporting Institution
Ministry of Research, Innovation and Digitization, CNCS-UEFISCDI
Project Number
PN-III-P4-PCE-2021-1881,
References
- [1] Agashe, N.S.: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. Pure Appl. Math. 23, 399–409 (1992).
- [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] Chen, B.-Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimentions. Glasgow Math. J. 41, 33–41 (1999).
- [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] Friedmann, A.; Schouten, J.A.: Über die Geometrie der halbsymmetrischen Übertragungen. Math. Z. 21, 211–223 (1924).
- [6] Hayden, H.: Subspaces of a space with torsion. Proc. London Math. Soc. 34, 27–50 (1932).
- [7] Imai, T.: Notes on semi-symmetric metric connections. Tensor 24, 293–296 (1972).
- [8] Mihai, A.: A note on derived connections from semi-symmetric metric connections. Math. Slovaca 67(1), 221–226 (2017).
- [9] Nakao, Z.: Submanifolds of a Riemannian manifold with semisymmetric metric connections. Proc. Amer. Math. Soc. 54, 261–266 (1976).
- [10] Opozda, B.: A sectional curvature for statistical structures. Linear Alg. Appl. 497, 134–161 (2016).
- [11] Schouten, J.A.: Ricci-Calculus. An Introduction to Tensor Analysis and its Geometrical Applications. Springer-Verlag, Berlin (1954).
- [12] Toader, A.M.; Buta, M.C.; Cimpoesu, F.; Mihai, A.: The holohedrization effect in ligand field models. Symmetry 16(1), art.22 (2024).
- [13] Yano, K.: On semi symmetric metric connection. Rev. Roum. Math. Pures Appl. 15, 1579–1591 (1970).
Abstract
Project Number
PN-III-P4-PCE-2021-1881,
References
- [1] Agashe, N.S.: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. Pure Appl. Math. 23, 399–409 (1992).
- [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] Chen, B.-Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimentions. Glasgow Math. J. 41, 33–41 (1999).
- [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] Friedmann, A.; Schouten, J.A.: Über die Geometrie der halbsymmetrischen Übertragungen. Math. Z. 21, 211–223 (1924).
- [6] Hayden, H.: Subspaces of a space with torsion. Proc. London Math. Soc. 34, 27–50 (1932).
- [7] Imai, T.: Notes on semi-symmetric metric connections. Tensor 24, 293–296 (1972).
- [8] Mihai, A.: A note on derived connections from semi-symmetric metric connections. Math. Slovaca 67(1), 221–226 (2017).
- [9] Nakao, Z.: Submanifolds of a Riemannian manifold with semisymmetric metric connections. Proc. Amer. Math. Soc. 54, 261–266 (1976).
- [10] Opozda, B.: A sectional curvature for statistical structures. Linear Alg. Appl. 497, 134–161 (2016).
- [11] Schouten, J.A.: Ricci-Calculus. An Introduction to Tensor Analysis and its Geometrical Applications. Springer-Verlag, Berlin (1954).
- [12] Toader, A.M.; Buta, M.C.; Cimpoesu, F.; Mihai, A.: The holohedrization effect in ligand field models. Symmetry 16(1), art.22 (2024).
- [13] Yano, K.: On semi symmetric metric connection. Rev. Roum. Math. Pures Appl. 15, 1579–1591 (1970).
Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Project Number | PN-III-P4-PCE-2021-1881, |
| Early Pub Date | April 5, 2024 |
| Publication Date | April 23, 2024 |
| Submission Date | February 20, 2024 |
| Acceptance Date | March 4, 2024 |
| Published in Issue | Year 2024 |