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Optimal inequalities for submanifolds in statistical manifolds of quasi constant curvature

Bansal Pooja (Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India), poojabansal811@gmail.com
Uddin Siraj (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia), siraj.ch@gmail.com
Shahid Mohammad Hasan (Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India), hasan jmi@yahoo.com

In this paper, we establish B.-Y. Chen’s optimal inequalities for statistical submanifolds involving Casorati curvature and the normalized scalar curavture in a statistical manifold of quasi constant curvature. The equality cases of these inequalities are also considered. Further, we provide some applications of our results. Moreover, as a new example we construct minimal statistical surface (statistical submanifold) of a statistical manifold of quasi constant curvature.

Keywords: Statistical manifold, quasi constant curvature, dual connections, scalar curvature, sectional curvature