TY - JOUR T1 - A Note on a Well-Defined Sectional Curvature of a Semi-Symmetric Non-Metric Connection AU - Mihai, Adela AU - Mihai, Ion PY - 2024 DA - April Y2 - 2024 DO - 10.36890/iejg.1440523 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 15 EP - 23 VL - 17 IS - 1 LA - en AB - 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. KW - Linear connection KW - semi-symmetric connection KW - metric connection KW - non-metric connection KW - sectional curvature CR - [1] Agashe, N.S.: A semi-symmetric non-metric connection on a Riemannian manifold. Indian J. Pure Appl. Math. 23, 399–409 (1992). CR - [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). CR - [3] Chen, B.-Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimentions. Glasgow Math. J. 41, 33–41 (1999). CR - [4] Cimpoesu, F.; Mihai, A.: Characterizing the E ⊗ e Jahn-Teller potential energy surfaces by differential geometry tools, Symmetry 14(3), art 436 (2022). CR - [5] Friedmann, A.; Schouten, J.A.: Über die Geometrie der halbsymmetrischen Übertragungen. Math. Z. 21, 211–223 (1924). CR - [6] Hayden, H.: Subspaces of a space with torsion. Proc. London Math. Soc. 34, 27–50 (1932). CR - [7] Imai, T.: Notes on semi-symmetric metric connections. Tensor 24, 293–296 (1972). CR - [8] Mihai, A.: A note on derived connections from semi-symmetric metric connections. Math. Slovaca 67(1), 221–226 (2017). CR - [9] Nakao, Z.: Submanifolds of a Riemannian manifold with semisymmetric metric connections. Proc. Amer. Math. Soc. 54, 261–266 (1976). CR - [10] Opozda, B.: A sectional curvature for statistical structures. Linear Alg. Appl. 497, 134–161 (2016). CR - [11] Schouten, J.A.: Ricci-Calculus. An Introduction to Tensor Analysis and its Geometrical Applications. Springer-Verlag, Berlin (1954). CR - [12] Toader, A.M.; Buta, M.C.; Cimpoesu, F.; Mihai, A.: The holohedrization effect in ligand field models. Symmetry 16(1), art.22 (2024). CR - [13] Yano, K.: On semi symmetric metric connection. Rev. Roum. Math. Pures Appl. 15, 1579–1591 (1970). UR - https://doi.org/10.36890/iejg.1440523 L1 - https://dergipark.org.tr/en/download/article-file/3743413 ER -