• 제목/요약/키워드: non-flat complex space forms

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REAL HYPERSURFACES IN A NON-FLAT COMPLEX SPACE FORM WITH LIE RECURRENT STRUCTURE JACOBI OPERATOR

  • Kaimakamis, George;Panagiotidou, Konstantina
    • 대한수학회보
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    • 제50권6호
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    • pp.2089-2101
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    • 2013
  • The aim of this paper is to introduce the notion of Lie recurrent structure Jacobi operator for real hypersurfaces in non-flat complex space forms and to study such real hypersurfaces. More precisely, the non-existence of such real hypersurfaces is proved.

REAL HYPERSURFACES WITH MIAO-TAM CRITICAL METRICS OF COMPLEX SPACE FORMS

  • Chen, Xiaomin
    • 대한수학회지
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    • 제55권3호
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    • pp.735-747
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    • 2018
  • Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

PSEUDO-PARALLEL REAL HYPERSURFACES IN COMPLEX SPACE FORMS

  • Lobos, Guillermo A.;Ortega, Miguel
    • 대한수학회보
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    • 제41권4호
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    • pp.609-618
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    • 2004
  • Pseudo-parallel real hypersurfaces in complex space forms can be defined as an extrinsic analogues of pseudo-symmetric real hypersurfaces, that generalize the notion of semi-symmetric real hypersurface. In this paper a classification of the pseudo-parallel real hypersurfaces in a non-flat complex space forms is obtained.

ON THE LIE DERIVATIVE OF REAL HYPERSURFACES IN ℂP2 AND ℂH2 WITH RESPECT TO THE GENERALIZED TANAKA-WEBSTER CONNECTION

  • PANAGIOTIDOU, KONSTANTINA;PEREZ, JUAN DE DIOS
    • 대한수학회보
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    • 제52권5호
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    • pp.1621-1630
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    • 2015
  • In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.