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

Yıl 2018, Cilt: 11 Sayı: 1, 57 - 67, 30.04.2018

Aliya Naaz Siddiqui

Öz

In this paper, we establish two sharp inequalities, which involve the generalized normalized

δ-Casorati curvatures and the generalized normalized scalar curvature of any submanifold in

generalized Sasakian space forms with semi-symmetric metric connection by using T Oprea’s

technique. Afterwards, we examine that the equality holds if and only if the submanifold is

invariantly 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 ambient

space form with SSMC.

Anahtar Kelimeler

δ-Casorati Curvatures, bi-slant submanifold, generalized Sasakian space forms, semi-symmetric metric connection, quasi-umbilical submanifold

Kaynakça

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