Kyungpook Mathematical Journal

  • 제58권1호
  • /
  • Pages.167-182
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  • 2018
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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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)
  • 투고 : 2017.07.07
  • 심사 : 2018.02.08
  • 발행 : 2018.03.23
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초록

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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참고문헌

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