共查询到20条相似文献,搜索用时 31 毫秒
1.
Chikako Mese 《manuscripta mathematica》1999,100(3):375-389
In this paper, we study the structure of locally compact metric spaces of Hausdorff dimension 2. If such a space has non-positive
curvautre and a local cone structure, then every simple closed curve bounds a conformal disk. On a surface (a topological
manifold of dimension 2), a distance function with non-positive curvature and whose metric topology is equivalent to the surface
topology gives a structure of a Riemann surface. The construction of conformal disks in these spaces uses minimal surface
theory; in particular, the solution of the Plateau Problem in metric spaces of non-positive curvature.
Received: 18 November 1997/ Revised versions: 15 January and 7 June 1999 相似文献
2.
Miguel Sánchez 《Differential Geometry and its Applications》2006,24(1):21-32
Some results related to the causality of compact Lorentzian manifolds are proven: (1) any compact Lorentzian manifold which admits a timelike conformal vector field is totally vicious, and (2) a compact Lorentzian manifold covered regularly by a globally hyperbolic spacetime admits a timelike closed geodesic, if some natural topological assumptions (fulfilled, for example, if one of the conjugacy classes of deck transformations containing a closed timelike curve is finite) hold. As a consequence, any compact Lorentzian manifold conformal to a static spacetime is geodesically connected by causal geodesics, and admits a timelike closed geodesic. 相似文献
3.
We treat n-dimensional compact minimal submanifolds of complex projective space when the maximal holomorphic tangent subspace is (n − 1)-dimensional and we give a sufficient condition for such submanifolds to be tubes over totally geodesic complex subspaces.
Authors’ addresses: Mirjana Djorić, Faculty of Mathematics, University of Belgrade, Studentski trg 16, pb. 550, 11000 Belgrade,
Serbia; Masafumi Okumura, 5-25-25 Minami Ikuta, Tama-ku, Kawasaki, Japan 相似文献
4.
Large volume growth and the topology of open manifolds 总被引:2,自引:0,他引:2
Changyu Xia 《Mathematische Zeitschrift》2002,239(3):515-526
In this paper, we study complete noncompact Riemannian manifolds with nonnegative Ricci curvature and large volume growth.
We find some reasonable conditions to insure that this kind of manifolds are diffeomorphic to a Euclidean space or have finite
topological type.
Received: January 4, 2000; in final form: October 31, 2000 / Published online: 19 October 2001 相似文献
5.
In [T. Kimura, M.S. Tanaka, Totally geodesic submanifold in compact symmetric spaces of rank two, Tokyo J. Math., in press], the authors obtained the global classification of the maximal totally geodesic submanifolds in compact connected irreducible symmetric spaces of rank two. In this paper, we determine their stability as minimal submanifolds in compact symmetric spaces of rank two. 相似文献
6.
We study complete minimal surfaces M immersed in R
3, with finite topology and one end. We give conditions which oblige M to be conformally a compact Riemann surface punctured in one point, and we show that M can be parametrized by meromorphic data on this compact Riemann surface. The goal is to prove that when M is also embedded, then the end of M is asymptotic to an end of a helicoid (or M is a plane).
Received: 13 January 1997 / Revised version: 15 September 1997 相似文献
7.
We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by
a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space
of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous
space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry
of these spaces, in particular of non-negatively curved homogeneous spaces.
Dedicated to the memory of A. D. Alexandrov 相似文献
8.
Claudio Gorodski 《Geometriae Dedicata》1994,53(1):75-102
The purpose of this paper is to pursue to work initiated by Hsiang-Lawson and study cohomogeneity 1 minimal hypersurfaces in Euclidean spheres which are equivariant under the linear isotropy representation of a rank 3 compact symmetric space.Supported by the grant NSF DMS 90-01089 and by CNPq (Brazil) 相似文献
9.
Knut Smoczyk 《Mathematische Zeitschrift》2002,240(4):849-883
We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. .
Received: 11 April 2001 / Published online: 29 April 2002 相似文献
10.
Mohammed Guediri 《Mathematische Zeitschrift》2002,239(2):277-291
In [19], Tipler has shown that a compact spacetime having a regular globally hyperbolic covering space with compact Cauchy
surfaces necessarily contains a closed timelike geodesic. The restriction to compact spacetimes with just regular globally
hyperbolic coverings (i.e., the Cauchy surfaces are not required to be compact) is still an open question. Here, we shall
answer this question negatively by providing examples of compact flat Lorentz space forms without closed timelike geodesics,
and shall give some criterion for the existence of such geodesics. More generally, we will show that in a compact spacetime
having a regular globally hyperbolic covering, each free timelike homotopy class determined by a central deck transformation
must contain a closed timelike geodesic. Whether or not a compact flat spacetime contains closed nonspacelike geodesics is,
as far as we know, an open question. We shall answer this question affirmatively. We shall also introduce the notion of timelike
injectivity radius for a spacetime relative to a free timelike homotopy class and shall show that it is finite whenever the
corresponding deck transformation is central.
Received: 9 November 1999; in final form: 19 September 2000 / Published online: 25 June 2001 相似文献
11.
Y. S. Poon 《Geometriae Dedicata》1996,60(1):49-64
We classify compact anti-self-dual Hermitian surfaces and compact four-dimensional conformally flat manifolds for which the group of orientation preserving conformal transformations contains a two-dimensional torus. As a corollary, we derive a topological classification of compact self-dual manifolds for which the group of conformal transformations contains a two-dimensional torus.Partially supported by the National Science Foundation grant DMS-9306950. 相似文献
12.
Claudio Gorodski 《Bulletin of the Brazilian Mathematical Society》1996,27(1):1-22
We describe a method to construct embedded, minimal hyperspheres in rank two compact symmetric spaces which are equivariant under the isotropy action of the symmetric space, and we supply the details of the construction for the exceptional Lie groupG
2.Partially supported by CNPq (brazil) 相似文献
13.
We prove that for each minimal rotation on a compact metric group and each topological cocycle , either φ is a topological coboundary, or is topologically ergodic, or the partition into orbits is the decomposition of into minimal components. As an application, we generalize a result by Glasner and show that if is a minimal topologically weakly mixing flow, then whenever φ is universally ergodic the minimal map
is not PI but is disjoint from all minimal topologically weakly mixing systems.
(Received 14 June 1999; in final form 28 September 2001) 相似文献
14.
LetM be a compact Riemannian manifold with smooth boundary M. We get bounds for the first eigenvalue of the Dirichlet eigenvalue problem onM in terms of bounds of the sectional curvature ofM and the normal curvatures of M. We discuss the equality, which is attained precisely on certain model spaces defined by J. H. Eschenburg. We also get analog results for Kähler manifolds. We show how the same technique gives comparison theorems for the quotient volume(P)/volume(M),M being a compact Riemannian or Kähler manifold andP being a compact real hypersurface ofM.Work partially supported by a DGICYT Grant No. PB94-0972 and by the E.C. Contract CHRX-CT92-0050 GADGET II. 相似文献
15.
A vector field X on a Riemannian manifold determines a submanifold in the tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. When M is compact, the volume is well defined and, usually, this functional is studied for unit fields. Parallel vector fields are trivial minima of this functional.For manifolds of dimension 5, we obtain an explicit result showing how the topology of a vector field with constant length influences its volume. We apply this result to the case of vector fields that define Riemannian foliations with all leaves compact.Received: 29 April 2004 相似文献
16.
Jaeman Kim 《Monatshefte für Mathematik》2007,152(3):251-254
We show that every compact Einstein Hermitian surface with constant *–scalar curvature is a K?hler surface. In contrast to
the 4-dimensional case, it is shown that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold with constant *–scalar curvature which is not K?hler.
This study is supported by Kangwon National University. 相似文献
17.
Neil N. Katz 《Differential Geometry and its Applications》2005,22(3):297-313
We study a broad class of problems where volume is minimized among metrics on a smooth, compact Riemannian manifold that keep the length of a fixed set of curves bounded below. They can be seen as a generalization of isosystolic inequalities. Necessary and sufficient conditions are given for continuous minima in a conformal class and necessary conditions are given for local minima. 相似文献
18.
Sung Ho Wang 《Differential Geometry and its Applications》2005,23(3):351-360
A canonical real line bundle associated to a minimal Lagrangian submanifold in a Kähler-Einstein manifold X is known to be special Lagrangian when considered as a subset of the canonical line bundle of X with a natural Calabi-Yau structure. We first verify this result by standard moving frame computation, and obtain a uniform lower bound for the mass of compact minimal Lagrangian submanifolds in CPn. Similar correspondence is then proved for integrable G2 and Spin(7) structures on the bundle of anti self dual 2-forms and a Spin bundle respectively of a self dual Einstein 4-manifold N constructed by Bryant and Salamon. In this case, analogues of tangent and normal bundles of certain minimal surfaces in N are calibrated, i.e., associative, coassociative, or Cayley. 相似文献
19.
Kazuo Akutagawa 《Mathematische Zeitschrift》2003,243(1):85-98
For a supergroup , we describe an obstruction to the existence of positive scalar curvature metrics with minimal boundary condition on a compact
n-dimensional -manifold W with nonempty boundary M, , in terms of the bordism class [M] in the Stolz obstruction group associated to [St2]. In par ticular, when W is a 5-dimensional spin manifold and the -invariant of a connected component of M is nonzero, we prove that W does not admit a positive scalar curvature metric with minimal boundary condition.
Received: 4 July 2001; in final form: 5 February 2002 / Published online: 8 November 2002
RID="*"
ID="*" Partially supported by the Grants-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, No.
11640070. 相似文献
20.
Paola Matzeu 《Monatshefte für Mathematik》2002,136(4):297-311
We consider compact Weyl submanifolds of Weyl flat manifolds with special attention on compact Einstein-Weyl hypersurfaces.
In particular, in the last part of the paper, we study Weyl submanifolds of special noncompact manifolds, called PC-manifolds.
Received July 16, 2001; in revised form February 6, 2002 Published online August 9, 2002 相似文献