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1.
On a real hypersurface in a Kähler manifold we can consider a natural closed 2-form associated with the almost contact metric structure induced by Kähler structure. Contrary to real hypersurfaces of type (A), on real hypersurfaces of type (B) in a complex hyperbolic space we show that non-geodesic trajectories under Sasakian magnetic fields, which are constant multiples of the natural closed 2-form, are not curves of order 2. 相似文献
2.
A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous
functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker.
Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which
normally depend upon uniform convergence of series of continuous functions. We also establish a Tietze-type extension theorem
characterizing closed G
δ
-sets in a normal space.
This research was supported by the Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02.
The first named author also acknowledges financial support from the University of the Basque Country under grant UPV05/101. 相似文献
3.
Ruled real hypersurfaces of complex space forms are investigated by using the fact that such hypersurfaces can be constructed by moving a 1-codimensional complex totally geodesic submanifold of the ambient space along a curve. Among other results, a classification of minimal ruled real hypersurfaces and an example of a homogeneous ruled real hypersurface are given. 相似文献
4.
We consider closed biharmonic hypersurfaces in a Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic hypersurfaces in space forms. As an application of this formula, we reobtain a result concerning the closed biharmonic hypersurfaces in Euclidean spheres that lie in a closed hemisphere. 相似文献
5.
We consider closed hypersurfaces of the sphere with scalar curvature one, prove a gap theorem for a modified second fundamental
form and determine the hypersurfaces that are at the end points of the gap. As an application we characterize the closed,
two-sided index one hypersurfaces with scalar curvature one in the real projective space.
Received: October 12, 2001 相似文献
6.
We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms. In particular, we explain the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator. This constitutes the following natural step after Kimura and Berndt?s classifications of Hopf real hypersurfaces with constant principal curvatures in complex space forms. 相似文献
7.
We establish an inequality among the Ricci curvature, the squared mean curvature, and the normal curvature for real hypersurfaces in complex space forms. We classify real hypersurfaces in two-dimensional non-flat complex space forms which admit a unit vector field satisfying identically the equality case of the inequality. 相似文献
8.
A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere. In this paper, we study intrinsic geometry of Lie hypersurfaces, such as Ricci curvatures, scalar curvatures, and sectional curvatures. 相似文献
9.
We characterize all totally η-umbilic hypersurfaces and ruled real hypersurfaces in nonflat complex space forms and certain real hypersurfaces of type
(A2) in complex projective spaces by using the property that some of their geodesics are mapped to circles of the same curvature
in these ambient spaces. 相似文献
10.
The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel. 相似文献
11.
A. V. Loboda 《Functional Analysis and Its Applications》2000,34(2):106-113
In the paper, a classification of real hypersurfaces of the space ℂ2 that admit transitive actions of local Lie groups of holomorphic transformations is constructed.
Any nonspherical Levi nondegenerate homogeneous surface is determined by the triple of real coefficientsN
520
2
,N
440, ImN
421 of a Moser normal equation. All such surfaces are described by several quadratic curves in the space of above coefficcients.
This work was partially supported by RFBR grant 96-01-01002.
Voronezh State Academy of Architecture and Civil Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol.
34, No. 2, pp. 33–42, April–June, 2000.
Translated by A. V. Loboda 相似文献
12.
Summary We classifyD-Einstein real hypersurfaces of quaternionic space forms, obtaining as a consequence the non-existence of Ricci-parallel real
hypersurfaces in the quaternionic hyperbolic space.
Entrata in Redazione il 12 dicembre 1997 e, in versione riveduta, il 18 maggio 1998. 相似文献
13.
M. Ortega 《Acta Mathematica Hungarica》2002,93(3):225-242
A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturally when we consider such families of tangent planes. We are able to classify real hypersurfaces in quaternionic space forms satisfying these definitions. 相似文献
14.
In this paper, we study closed k-maximal spacelike hypersurfaces M
n
in anti-de Sitter space H
1
n+1 (−1) with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
The first author was supported by Japan Society for Promotion of Science. The third author was supported by grant Proj. No.
R17-2008-001-01000-0 from Korea Science & Engineering Foundation. 相似文献
15.
The main purpose of this paper is to give basic properties of real lightlike hypersurfaces of paraquaternionic manifold and
to prove the nonexistence of real lightlike hypersurfaces in paraquaternionic space forms under some conditions.
Dedicated to the memory of Professor Aldo Cossu 相似文献
16.
Integral curves of characteristic vector fields of real hypersurfaces in nonflat complex space forms
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.
相似文献
17.
We consider the closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using an integral formula or Brendle's Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These results can be viewed as generalizations of the classical Jellet-Liebmann theorem and the Alexandrov theorem in Euclidean space. 相似文献
18.
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.The first author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540075), Ministry of Education, Science, Sports and Culture.The second author was partially supported by Grant-in-Aid for Scientific Research (C) (No. 14540080), Ministry of Education, Science, Sports and Culture. 相似文献
19.
In this paper we present a general patchworking procedure for the construction of reduced singular curves having prescribed
singularities and belonging to a given linear system on algebraic surfaces. It originates in the Viro “gluing” method for
the construction of real non-singular algebraic hypersurfaces. The general procedure includes almost all known particular
modifications, and goes far beyond. Some applications and examples illustrate the construction.
Both authors were partially supported by the Herman Minkowsky-Minerva Center for Geometry at Tel Aviv University, and by grant
no. G-616-15.6/99 from the German-Israeli Foundation for Research and Development. The first author was also supported by
the Bessel Research Award from the Alexander von Humboldt Foundation. The second author was also partially supported by the
EC-network ‘Algebraic Lie Representations” contract no. ERB-FMRX-CT97-0100. 相似文献
20.
This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse
image by the Hopf fibration of a real hypersurface M in complex space form M
m(4ε). In the second, we give a complete classification of real hypersurfaces in M
m(4ε) which satisfy the above geometric facts.
The second author was supported by DGICYT research project BFM 2001-2871-C04-01 and the first and the third authors were supported
by grant Proj. No. R14-2002-003-01001-0 from Korea Research Foundation, Korea 2006. 相似文献