Geodesic
Lower Extremities for Generalized Normalized $\delta$-Casorati Curvatures of Bi-slant Submanifolds in Generalized Complex Space Forms
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 591 .

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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.
Classification : 53B05 53B20, 53C40
Keywords: Casorati curvature, generalized complex space form, scalar curvature, warped product 
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     author = {Mohd. Aquib and Mohammad Hasan Shahid and Mohammed Jamali},
     title = {Lower {Extremities} for {Generalized} {Normalized} $\delta${-Casorati} {Curvatures} of {Bi-slant} {Submanifolds} in {Generalized} {Complex} {Space} {Forms}},
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Mohd. Aquib; Mohammad Hasan Shahid; Mohammed Jamali. Lower Extremities for Generalized Normalized $\delta$-Casorati Curvatures of Bi-slant Submanifolds in Generalized Complex Space Forms. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 591 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a10/