• 제목/요약/키워드: Ricci-parallel hypersurface

검색결과 18건 처리시간 0.016초

ξ-PARALLEL STRUCTURE JACOBI OPERATORS OF REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM

  • KIM, NAM-GIL;KI, U-HANG
    • 호남수학학술지
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    • 제28권4호
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    • pp.573-589
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    • 2006
  • Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.

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REAL HYPERSURFACES WITH ξ-PARALLEL RICCI TENSOR IN A COMPLEX SPACE FORM

  • Ahn, Seong-Soo;Han, Seung-Gook;Kim, Nam-Gil;Lee, Seong-Baek
    • 대한수학회논문집
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    • 제13권4호
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    • pp.825-838
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    • 1998
  • We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽$_{ξ/}$S = 0 and Sξ = $\sigma$ξ for a smooth function $\sigma$, then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.

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REAL HYPERSURFACES OF A QUATERNIONIC PROJECTIVE SPACE IN TERMS OF RICCI TENSOR

  • Choe, Yeong-Wu;Choe, Eun-Kyung
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제11권3호
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    • pp.197-206
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    • 2004
  • We obtain some characterizations of a pseudo Ricci-parallel real hypersurface in a quaternionic projective space $QP^{n}$ and find the condition that M is locally congruent to a geodesic hypersphere of $QP^{n}$ .

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NONEXISTENCE OF RICCI-PARALLEL REAL HYPERSURFACES IN P2C OR H2C

  • Kim, Un-Kyu
    • 대한수학회보
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    • 제41권4호
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    • pp.699-708
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    • 2004
  • Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is "Are there any Ricci-parallel real hypersurfaces in complex projective space $P_2C$ or complex hyperbolic space $H_2C$\ulcorner" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

Ricci Semi-Symmetric Lightlike Hypersurfaces of an Indefinite Cosymplectic Space Form

  • Gupta, Ram Shankar
    • Kyungpook Mathematical Journal
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    • 제53권4호
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    • pp.593-602
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    • 2013
  • This paper is devoted to study Ricci semi-symmetric lightlike hypersurfaces of an indefinite cosymplectic space form with structure vector field tangent to hypersurface. The condition for Ricci tensor of lightlike hypersurface of indefinite cosymplectic space form to be semi-symmetric and parallel have been obtained. An example of non-totally geodesic Ricci semi-symmetric lightlike hypersurface in $R^7_2$ have been given.

Structure Eigenvectors of the Ricci Tensor in a Real Hypersurface of a Complex Projective Space

  • Li, Chunji;Ki, U-Hang
    • Kyungpook Mathematical Journal
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    • 제46권4호
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    • pp.463-476
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    • 2006
  • It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

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SOME CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE (A) IN A NONFLAT COMPLEX SPACE FORM

  • Ki, U-Hang;Liu, Hui-Li
    • 대한수학회보
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    • 제44권1호
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    • pp.157-172
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    • 2007
  • In this paper, we prove that if the structure Jacobi operator $R_{\xi}-parallel\;and\;R_{\xi}$ commutes with the Ricci tensor S, then a real hypersurface with non-negative scalar curvature of a nonflat complex space form $M_{n}(C)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_{n}(C)$.

CHARACTERIZATIONS OF REAL HYPERSURFACES OF COMPLEX SPACE FORMS IN TERMS OF RICCI OPERATORS

  • Sohn, Woon-Ha
    • 대한수학회보
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    • 제44권1호
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    • pp.195-202
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    • 2007
  • We prove that a real hypersurface M in a complex space form Mn(c), $c{\neq}0$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution and the Ricci operator is ${\eta}-parallel$, is a Hopf hypersurface. We also give a characterization of this hypersurface.

REAL HYPERSURFACES IN COMPLEX SPACE FORMS WITH ε-PARALLEL RICCI TENSOR AND STRUCTURE JACOBI OPERATOR

  • Ki, U-Hang;Perez Juan De Dios;Santos Florentino G.;Suh Young-Jin
    • 대한수학회지
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    • 제44권2호
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    • pp.307-326
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    • 2007
  • We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces M in a nonflat complex space form $M_n(c)$ under the condition that ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ respectively denote the Ricci tensor and the structure Jacobi operator of M in $M_n(c)$.

EQUIVALENCE CONDITIONS OF SYMMETRY PROPERTIES IN LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

  • Lungiambudila, Oscar;Massamba, Fortune;Tossa, Joel
    • 대한수학회보
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    • 제53권4호
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    • pp.1259-1280
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    • 2016
  • The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.