A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form

Volume 54 / 2006

Takehiro Itoh, Sadahiro Maeda Bulletin Polish Acad. Sci. Math. 54 (2006), 125-136 MSC: Primary 53B25; Secondary 53C40. DOI: 10.4064/ba54-2-4


We characterize totally $\eta$-umbilic real hypersurfaces in a nonflat complex space form $\widetilde{M}_n(c)$ $(=\Bbb CP^n(c)$ or $\Bbb CH^n(c))$ and a real hypersurface of type $(A_2)$ of radius $\pi/(2\sqrt{c})$ in $\Bbb CP^n(c)$ by observing the shape of some geodesics on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).


  • Takehiro ItohFaculty of Education
    Shinshu University
    6-ro, Nishi-Nagano, Nagano 380-8544, Japan
  • Sadahiro MaedaDepartment of Mathematics
    Shimane University
    Matsue, Shimane, 690-8504, Japan

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