Lower Extremities for Generalized Normalized $\delta$-Casorati Curvatures of Bi-slant Submanifolds in Generalized Complex Space Forms


Mohd. Aquib, Mohammad Hasan Shahid, Mohammed Jamali




In this paper, we obtain the inequalities for the generalized normalized $\delta$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized complex space form, which is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form and characterizes the submanifolds on which equalities hold. We also develop, the same inequalities for semi-slant, hemi-slant, CR, slant, invariant and anti-invariant submanifolds in the same target space and consider the equality case. Moreover, we obtain a geometric inequality involving Casorati curvature for warped product bi-slant submanifolds in same ambient and obtain an obstruction result.