INEQUALITIES FOR GENERALIZED NORMALIZED $\delta$-CASORATI CURVATURES OF SLANT SUBMANIFOLDS IN QUATERNIONIC SPACE FORMS

By Jaewon Lee, Gabriel Eduard Vîlcu. 2014

67 citations recorded by the source corpus.

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized $\delta$-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the  Casorati curvature for a slant submanifold in a quaternionic space form obtained by Slesar et al., J. Inequal. Appl. , 2014, 2014:123.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82bfe7e6469491e98ac2247a8602eaf3a89370e5

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In Applied Mathematics

1. Jae Won Lee
2. Chul Woo Lee
3. Gabriel Eduard Vîlcu
4. Liangdi Zhang
5. Pan Zhang

In Mathematical Physics

1. Jae Won Lee
2. Chul Woo Lee
3. Gabriel Eduard Vîlcu
4. Liangdi Zhang
5. Pan Zhang

Citations in the corpus

• Inequalities for casorati curvatures of submanifolds in real space forms (2014, methodology): “Following [16],wede ne the normalized δ-Casorati curvature δC(n − 1) by [δC(n − 1)]x = 1 2 Cx + n + 1 2n inf {C(L) | L a hyperplane of TxM}.”
• Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms (2017, methodology): “The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form; see [10; 11; 18; 20; 21].”