Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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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)
  • Received : 2017.07.07
  • Accepted : 2018.02.08
  • Published : 2018.03.23
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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.

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References

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