• Title/Summary/Keyword: complex projective space

Search Result 61, Processing Time 0.02 seconds

On generic submanifolds of a complex projective space

  • Seong Baek Lee;Seung Gook Han;Nam Gil Kim;Seong Soo Ahn
    • Communications of the Korean Mathematical Society
    • /
    • v.11 no.3
    • /
    • pp.743-756
    • /
    • 1996

  • The purpose of this paper is to compute the covariant derivative of a shape operator of a generic submanifold of a complex space form without using the Green-Stoke's theorem. In particular, we classify complete generic submanifolds of a complex number space $C^m$ with parallel mean curvature vector satisfying a certain condition.

  • PDF

CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR

  • Kim, Nam-Gil;Ki, U-Hang;Kurihara, Hiroyuki
    • Honam Mathematical Journal
    • /
    • v.30 no.3
    • /
    • pp.535-550
    • /
    • 2008

  • Let M be a real hypersurface of a complex space form with almost contact metric structure $({\phi},{\xi},{\eta},g)$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In particular, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex: projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant and not equal to -c/24 on M, where c is a constant holomorphic sectional curvature of a complex space form.

  • https://doi.org/10.5831/HMJ.2008.30.3.535 인용 PDF