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53B25, Local submanifolds — 5 results found.

      
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The Parallelism of a Certain Tensor of Real Hypersurfaces in a Nonflat Complex Space Form
C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (3) 2015, pp. 81-88
Tatsuyoshi Hamada; Katsufumi Yamashita (Received: 2014/10/15, Revised: 2014/11/04)

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In Theorem 1, we show a new condition for a real hypersurface \(M\) isometrically immersed into a nonflat complex space form to be a hypersurface of type (A). This condition is expressed by the parallelism of a certain tensor of type (1, 1) on \(M\) . Furthermore, using the discussion in the proof of Theorem 1, we can give a condition for a Kähler manifold to be a complex space form (see Theorem 2).

Dans le théorème 1, nous donnons une nouvelle condition pour qu’une hypersurface réelle \(M\) immergée dans une “space form” complexe non plate soit une hypersurface de type (A). Cette condition est exprimée par le parallélisme d’un certain tenseur de type (1, 1) sur \(M\) . De plus, en utilisant la discussion dans la démonstration du théorème 1, nous donnons une condition pour qu’une variété de Kähler soit une “space form” complexe (voir le théorème 2).

Nonnegatively Curved Geodesic Spheres in a Complex Hyperbolic Space
C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (3) 2013, pp. 114–120
Sadahiro Maeda (Received: 2013/05/01, Revised: 2013/09/15)

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We characterize geodesic spheres with sufficiently small radii in a complex hyperbolic space by using their geometric properties. These geodesic spheres are the only examples of hypersurfaces of type (A) having nonnegative sectional curvature in this ambient space.

Nous caractérisons les sphères géodésiques de rayon suffisamment petit dans un espace hyperbolique complexe en utilisant leurs propriétés géométriques. Ces sphères géodésiques sont les seuls exemples d’hypersurfaces de type (A) qui ont courbure non-negative dans cet espace ambiant.

Characterization of complex space forms in terms of characteristic vector fields on geodesic spheres
C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (4) 2006, pp. 114–120
Sadahiro Maeda (Received: 2006/05/30)

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Investigating geometric properties of characteristic vector fields on geodesic spheres in a complex space form, we characterize complex space forms in the class of Kähler manifolds.

En étudiant des propriétés géométriques de champs de vecteurs caractéristiques sur des sphères géodésiques dans un espace complexe à courbure constante, on caractérise ces espaces dans la classe des variétés kähleriennes.

A Congruence Theorem of Geodesies on Some Naturally Reductive Riemannian Homogeneous Manifolds
C. R. Math. Rep. Acad. Sci. Canada Vol. 26 (1) 2004, pp. 11–17
T. Adachi / S. Ma (Received: 2003/06/03)

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No abstract available but the full text is online at the title link above.

A characterization of Veronese imbeddings into complex projective spaces by circles
C. R. Math. Rep. Acad. Sci. Canada Vol. 24 (2) 2002, pp. 61–66
K. Suizu / S. Maeda / T. Adachi (Received: 2001/06/04)

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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