Chen Inequalities for Submanifolds of Real Space Forms With a Semi-Symmetric Metric Connection

Abstract

In this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric metric connection, i.e., relations between the mean curvature associated with the semi-symmetric metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered.

Classification of ideal submanifolds of real space forms with type number≤2

“…Many interesting results in this respect were obtained by many geometers (see, for instance, [1,2,3,4,5,6,7,9,11,12,13,15,17,18]). On the other hand, the classification of ideal submanifolds in space forms remains a very challenging problem.…”

Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection

“…In [15,16], Mihai and Özgür established Chen inequalities for submanifolds of real, complex and Sasakian space forms endowed with semi-symmetric metric connections and in [17,18], Özgür and Murathan gave Chen inequalities for submanifolds of a locally conformal almost cosymplectic manifold and a cosymplectic space form endowed with semi-symmetric metric connections. On the other hand, Lee et al proved inequalities involving the Casorati curvature of submanifolds in real, complex and Sasakian space forms endowed with a semi-symmetric metric connection in [7,8].…”

Optimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed with Semi-Symmetric Non-Metric Connections

“…Mihai and Özgür [14,15] proved Chen's inequalities for submanifolds in a real space with a semi-symmetric metric connection, a complex space with a semi-symmetric metric connection and a Sasakian space form with a semi-symmetric metric connection. They also studied Chen's inequalities for submanifolds in a real space form endowed with a semi-symmetric non-metric connection [16].…”