• Title/Summary/Keyword: generalized (${\kappa}$, ${\mu}$)-space forms

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CERTAIN RESULTS ON CONTACT METRIC GENERALIZED (κ, µ)-SPACE FORMS

  • Huchchappa, Aruna Kumara;Naik, Devaraja Mallesha;Venkatesha, Venkatesha
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1315-1328
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    • 2019
  • The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.

Bounds for Generalized Normalized δ-Casorati Curvatures for Submanifolds in Generalized (κ, µ)-space Forms

  • Aquib, Mohd;Shahid, Mohammad Hasan
    • Kyungpook Mathematical Journal
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    • v.58 no.1
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    • pp.167-182
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    • 2018
  • 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.