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ABSTRACT: Our main theorem is a characterization of a totally geodesic Kähler immersion of a complex n-dimensional Kähler manifold M
n
into an arbitrary complex (n + p)-dimensional Kähler manifold
[(M)\tilde]n+p\tilde{M}_{n+p}
by observing the extrinsic shape of Kähler Frenet curves on the submanifold M
n
. Those curves are closely related to the complex structure of M
n
.
Monatshefte für Mathematik 05/2012; 149(3):233-242. · 0.62 Impact Factor
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ABSTRACT: In this paper, we study real hypersurfaces all of whose integral curves of characteristic vector fields are plane curves in
a nonflat complex space form.
Geometriae Dedicata 04/2012; 123(1):65-72. · 0.36 Impact Factor
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ABSTRACT: We characterize some real hypersurfaces in an n-dimensional nonflat complex space form
Mn(c)( = \mathbbCPn(c)or\mathbbCHn(c))M_{n}(c)(= {\mathbb{C}}P^{n}(c)\,\, {\rm or}\, \, {\mathbb{C}}H^{n}(c)) in terms of Sasakian curves on real hypersurfaces which are closely related to their almost contact metric structures induced
from the ambient space Mn(c). We also classify curves on a geodesic sphere of
\mathbbCPn(c){\mathbb{C}}P^{n}(c) which are mapped to circles on some standard sphere through the well-known isometric embedding, and show that these curves
are Sasakian curves on this geodesic sphere.
Mathematics Subject Classification (2000).Primary 53C40-Secondary 53C22
Keywords.Nonflat complex space forms-real hypersurfaces-hypersurfaces of type (A)-Sasakian curves-structure torsion-normal curvature-geodesic spheres-the first standard minimal embedding-Euclidean spheres-homogeneous curves
Results in Mathematics 04/2012; 56(1):489-499. · 0.44 Impact Factor
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ABSTRACT: We give a necessary and sufficient condition for a Kähler manifold of complex dimension n ≧ 2 to be a complex space form in terms of its sectional curvatures, which is an extension of Schur’s lemma. Our study is
related to a congruence theorem for circles in a complex space form
Archiv der Mathematik 01/2008; 90(2):163-172. · 0.43 Impact Factor
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ABSTRACT: In this paper, we characterize hypersurfaces of type A2 in a complex projective space in terms of their geodesics.
Bulletin of the Australian Mathematical Society 01/2008; 77(01):1 - 8. · 0.55 Impact Factor
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ABSTRACT: In this paper we construct many ruled real hypersurfaces in a nonflat quaternionic space form systematically, and in particular give an example of a homogeneous ruled real hypersurface in a quaternionic hyperbolic space. In the second half of this paper we characterize them by investigating the extrinsic shape of their geodesics. We also characterize curvature-adapted real hypersurfaces in nonflat quaternionic space forms from the same viewpoint.
Monatshefte für Mathematik 01/2005; 145(3):179-190. · 0.62 Impact Factor
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ABSTRACT: In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
Czechoslovak Mathematical Journal 01/2005; 55(1):203-207. · 0.26 Impact Factor
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ABSTRACT: In this paper we study the quaternionic distribution D{\cal D} of acurvature-adapted real hypersurface M with constant principalcurvatures in a quaternionic hyperbolic space
\mathbbH Hn \mathbb{H} H^{n} . Weinvestigate integrability conditions for some natural distribution determined by means of principal distributions contained in thedistribution D{\cal D} and give a characterization of these real hypersurfaces in
\mathbbH Hn \mathbb{H} H^{n} .
Journal of Geometry 11/2002; 75(1):1-14.
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ABSTRACT: We give a survey of our recent results [KM, MA, Su, SMA] on sub-manifolds from the viewpoint of curves of order 2. We characterize some of nice submanifolds by the extrinsic shape of circles.
Series B: Mathematical Science. 01/2002; 35:1-21.
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ABSTRACT: In this article we treat a complex projective space CP n of constant holomorphic sectional curvature 4 as a model space. By using submanifold theory of CP n we shall investigate geometric properties about curves generated by some Killing vector fields on this space.
Series B: Mathematical Science. 01/2001; 34:61-85.
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ABSTRACT: In this note we study helices in a complex projective space. We char-acterize complex projective spaces among Hermitian symmetric spaces by the prop-erty that all holomorphic circles are closed. We also give examples of helices with multiple points.
Series B: Mathematical Science. 01/1999; 32:1-8.
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manuscripta mathematica 04/1997; 93(1):267-272. · 0.43 Impact Factor
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ABSTRACT: This paper consists of two parts. One is to construct a class of helical geodesic equivariant immersions of orderd(⩾3), which are neither Kaehler nor totally real immersions, into complex projective spaces. The other is to show the basic
results about a helix in complex space forms.
Geometriae Dedicata 04/1989; 30(1):93-114. · 0.36 Impact Factor
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ABSTRACT: For Hopf hypersurfaces in a nonflat complex space form $M^n(c; \Bbb{C})$, integral curves of their characteristic vector fields are ''nice'' curves in the sense that their extrinsic shapes in $M^n(c; \Bbb{C})$ are K\"ahler circles. In this paper we mainly study geodesic spheres in a nonflat complex space form $M^n(c; \Bbb{C})$. On these geodesic spheres we classify smooth curves whose extrinsic shapes are K\"ahler circles in $M^n(c; \Bbb{C}),c\not=0$. We also give a characterization of complex space forms among K\"ahler manifolds by extrinsic shapes of integral curves of characteristic vector fields on their geodesic spheres.
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ABSTRACT: Let Pn(C) be an n-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature 4, and let M be a real hypersurface of Pn(C). M has an almost contact metric structure ... http://www.tulips.tsukuba.ac.jp/mylimedio/dl/page.do?issueid=185629&tocid=100000305&page=547-561
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ABSTRACT: Real hypersurfaces in a complex projective space have been studied by many differential geometers (for example, see [1], [2], [3], [7], [14] and [15]). In this paper, we study real hypersurfaces in Pn(C) from the point of view of holomorphic distribution, ... http://www.tulips.tsukuba.ac.jp/mylimedio/dl/page.do?issueid=184118&tocid=100000227&page=39-52
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