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Abstrakty
We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form [...](c) (= CPn(c) or CHn(c)) and a real hypersurface of type (A2) of radius π/(2√c) in CPn(c) by observing the shape of some geodesies on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).
Wydawca
Rocznik
Tom
Strony
125--136
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
autor
- Faculty of Education Shinshu University, 6-ro, Nishi-Nagano, Nagano 380-8544, Japan, takehir@gipnc.shinshu-u.ac.jp
Bibliografia
- [AKM1] T. Adachi, M. Kimura and S. Maeda, A characterization of all homogeneous real hypersurfaces in a complex projective space by observing the extrinsic shape of geodesies, Arch. Math. (Basel) 73 (1999), 303-310.
- [AKM2] —, —, —, Real hypersurfaces some of whose geodesies are plane curves in nonflat complex space forms, Tohoku Math. J. 57 (2005), 223-230.
- [CM] B. Y. Chen and S. Maeda, Hopf hypersurfaces with constant principal curvatures in complex projective or complex hyperbolic spaces, Tokyo J. Math. 24 (2001),133-152.
- [FS] D. Ferus and S. Schirrmacher, Submanifolds in Euclidean space with simple geodesies, Math. Ann. 260 (1982), 57-62.
- [M] S. Maeda, Real hypersurfaces of complex projective spaces, ibid. 263 (1983), 473-478.
- [MO] S. Maeda and K. Ogiue, Characterizations of geodesic hyperspheres in a complex projective space by observing the extrinsic shape of geodesies, Math. Z. 225 (1997), 537-542.
- [NR] R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, in: Tight and Taut Submanifolds, T. E. Cecil and S. S. Chern (eds.), Cambridge Univ. Press, 1998, 233-305.
- [OT] K. Ogiue and R. Takagi, A submanifold which contains many extrinsic circles,Tsukuba J. Math. 8 (1984), 171-182.
- [S] K. Sakamoto, Planar geodesic immersions, Tdhoku Math. J. 29 (1977), 25-56.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0011-0022