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http://dx.doi.org/10.5666/KMJ.2018.58.1.167

Bounds for Generalized Normalized δ-Casorati Curvatures for Submanifolds in Generalized (κ, µ)-space Forms  

Aquib, Mohd (Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia)
Shahid, Mohammad Hasan (Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia)
Publication Information
Kyungpook Mathematical Journal / v.58, no.1, 2018 , pp. 167-182 More about this Journal
Abstract
In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.
Keywords
Casorati curvature; generalized (${\kappa},{\mu}$)-space forms; normalized scalar curvature;
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Times Cited By KSCI : 2  (Citation Analysis)
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