Geodesic
A Useful Characterization of Some Real Hypersurfaces in a Nonflat Complex Space Form
Takehiro Itoh1 ; Sadahiro Maeda2
1Faculty of Education Shinshu University 6-ro, Nishi-Nagano, Nagano 380-8544, Japan
2Department of Mathematics Shimane University Matsue, Shimane, 690-8504, Japan
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 2, pp. 125-136
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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).
DOI : 10.4064/ba54-2-4
Keywords: characterize totally eta umbilic real hypersurfaces nonflat complex space form widetilde bbb bbb real hypersurface type radius sqrt bbb observing shape geodesics those real hypersurfaces curves ambient manifolds theorems

Takehiro Itoh  1   ; Sadahiro Maeda  2

1 Faculty of Education Shinshu University 6-ro, Nishi-Nagano, Nagano 380-8544, Japan
2 Department of Mathematics Shimane University Matsue, Shimane, 690-8504, Japan 
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Takehiro Itoh; Sadahiro Maeda. A Useful Characterization of Some Real Hypersurfaces in a 
Nonflat Complex Space Form. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) no. 2, pp. 125-136. doi: 10.4064/ba54-2-4

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