Upper Bound Inequalities for δ− Casorati Curvatures of Submanifolds in Generalized Sasakian Space Forms Admitting a Semi-Symmetric Metric Connection

Abstract

In this paper, we establish two sharp inequalities, which involve the generalized normalizedδ− Casorati curvatures and the generalized normalized scalar curvature of any submanifold ingeneralized Sasakian space forms with semi-symmetric metric connection by using T Oprea’stechnique. Afterwards, we examine that the equality holds if and only if the submanifold isinvariantly quasi-umbilical in both inequalities. We also develop these inequalities for invariant,anti-invariant, CR, slant, semi-slant, hemi-slant and bi-slant submanifolds in the same ambientspace form with SSMC.