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

Mohammad Hasan Shahid|Mohd Aquib
경북대학교 자연과학대학 수학과|2018.03|Kyungpook Mathematical Journal|제58권 제1호|pp. 167-182|DOI https://doi.org/10.5666/KMJ.2018.58.1.167

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참고문헌

키워드

Casorati curvaturegeneralized ( ĸµ )-space formsnormalized scalar curvature
주제분류수학

초록

In this paper, we prove the optimal inequalities for the generalized normalized δ-Casorati curvature and the normalized scalar curvature for di erent submanifolds ingeneralized ( ĸ, µ )-space forms. The proof is based on an optimization procedure involvinga quadratic polynomial in the components of the second fundamental form. We alsocharacterize the submanifolds on which equalities hold.

Abstract

In this paper, we prove the optimal inequalities for the generalized normalized δ-Casorati curvature and the normalized scalar curvature for di erent submanifolds ingeneralized ( ĸ, µ )-space forms. The proof is based on an optimization procedure involvinga quadratic polynomial in the components of the second fundamental form. We alsocharacterize the submanifolds on which equalities hold.

참고문헌 (13)

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  11. 이철우, "OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS", 대한수학회보, 52(5), pp.1631~1647 (2015), 대한수학회
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OPTIMAL INEQUALITIES FOR THE CASORATI CURVATURES OF SUBMANIFOLDS OF GENERALIZED SPACE FORMS ENDOWED WITH SEMI-SYMMETRIC METRIC CONNECTIONS윤대원, 이재원, 이철우, Gabriel-Eduard Vilcu대한수학회 · 대한수학회보2015 · 제52권 제5호Some inequalities on totally real submanifolds in locally conformal Kaehler space forms김영호, 윤대원, AlfonsoCarriazo대한수학회 · 대한수학회지2004 · 제41권 제5호Inequality for Totally Real Warped Products in Locally Conformal Kaehler Space Forms김영호, Dae Won Yoon경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2004 · 제44권 제4호Ricci curvature of submanifolds of an S-space form김정식, Mohit Kumar Dwivedi, Mukut Mani Tripathi대한수학회 · 대한수학회보2009 · 제46권 제5호Optimizations on totally real submanifolds of LCS-manifolds using Casorati curvaturesAliya Naaz Siddiqui, Mohammad Hasan Shahid대한수학회 · 대한수학회논문집2019 · 제34권 제2호Shape operator of slant submanifolds in Sasakian space forms김영호, 윤대원, 이철우대한수학회 · 대한수학회보2003 · 제40권 제1호

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