Optimal casorati inequalities on bi-slant submanifolds of generalized sasakian space forms

Aliya Naaz Siddiqui

Abstract


In this paper, we use T Oprea's optimization method to establish some optimal Casorati inequalities, which involve the normalized scalar curvature for bi-slant submanifolds of generalized Sasakian space forms. In the continuation, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical.

Keywords


Casorati curvature; bi-slant submanifold; generalized Sasakian space form; quasi-umbilical submanifold

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DOI: http://dx.doi.org/10.5556/j.tkjm.49.2018.2638

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