共查询到20条相似文献,搜索用时 31 毫秒
1.
We discuss the image of a natural homomorphism from the bounded cohomology to the ordinary cohomology of a manifold. We give a necessary and sufficient condition for a Haken 3-manifold M to have the property that any class in the nth cohomology of M is bounded if n > 1.The first author was partially supported by JSPS. 相似文献
2.
We show that ifM is the total space of a holomorphic bundle with base space a simply connected homogeneous projective variety and fibre and
structure group a compact complex torus, then the identity component of the automorphism group ofM acts trivially on the Dolbeault cohomology ofM. We consider a class of compact complex homogeneous spacesW, which we call generalized Hopf manifolds, which are diffeomorphic to S1 ×K/L whereK is a compact connected simple Lie group andL is the semisimple part of the centralizer of a one dimensional torus inK. We compute the Dolbeault cohomology ofW. We compute the Picard group of any generalized Hopf manifold and show that every line bundle over a generalized Hopf manifold
arises from a representation of its fundamental group. 相似文献
3.
Consider a hypermanifold M
0 of a Riemannian manifold N whose Riccicurvature is bounded from below. If M
0 is transversal to a conformalvector field on N, then conditions are given, such that the meancurvature evolution of M
0 with Dirichlet boundary conditions has asolution for all times. 相似文献
4.
Tomasz Filar 《代数通讯》2013,41(6):2380-2387
Vasquez showed that for any finite group G there exists a number n(G) such that for every flat Riemannian manifold M with holonomy group G there exists a fiber bundle T → M → N, where T is a flat torus and N is a flat manifold of dimension less than or equal to n(G). We show that n(H) ≤ n(G) if H Δ leftG or G = N ? H and use this result to describe groups with the Vasquez number equal to 2 or 3. 相似文献
5.
《代数通讯》2013,41(10):4395-4419
We are interested in effective computablility of enumerative problems on a flag manifold. We show that for each flag manifold M, there exists a formula that expresses the operator of integration along M by derivatives. Applications to the computation of degrees of some classical varieties are given. 相似文献
6.
Let M be a compact manifold without boundary and let N be a connected manifold without boundary. For each the set of k times continuously differentiable maps between M and N has the structure of a smooth Banach manifold where the underlying manifold topology is the compact-open topology. We provide a detailed and rigorous proof for this important statement which is already partially covered by existing literature. 相似文献
7.
Bang-yen Chen 《Monatshefte für Mathematik》1981,91(4):257-274
LetN be a real submanifold in a complex manifoldM. If the maximal complex subspaces of the tangent spaces ofM contained in the tangent spaces ofN are of constant dimension and they define a differentiable distribution, thenN is called a generic submanifold. The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds andCR-submanifolds. In this paper we initiate a study of generic submanifolds in a Kähler manifold from differential geometric point of view. Some fundamental results in this respect will be obtained. 相似文献
8.
Michael L. Mihalik 《Commentarii Mathematici Helvetici》1996,71(1):362-372
If a finitely presented groupG is negatively curved, automatic or asynchronously automatic thenG has an asynchronously bounded “almost prefix closed” combing. Results in [Br1] and [E] imply that the fundamental group of any closed 3-manifold satisfying Thurston's geometrization conjecture has an
asynchronously bounded, almost prefix closed combing.
MAIN THEOREM. IfM is a compactP
2-irreducible 3-manifold,π
1 (M) has an asynchronously bounded, almost prefix closed combing, andH, a subgroup ofπ
1 (M), is quasiconvex with respect to this combing, then the cover ofM corresponding toH is a missing boundary manifold. 相似文献
9.
Izu Vaisman 《Monatshefte für Mathematik》1990,109(4):305-310
IfM is a Riemannian manifold, andL is a Lagrangian submanifold ofT
*
M, the Maslov class ofL has a canonical representative 1-form which we call theMaslov form ofL. We prove that ifL =v
*
N = conormal bundle of a submanifoldN ofM, its Maslov form vanishes iffN is a minimal submanifold. Particularly, ifM is locally flatv
*
N is a minimal Lagrangian submanifold ofT
*
M iffN is a minimal submanifold ofM. This strengthens a result of Harvey and Lawson [H L]. 相似文献
10.
LetM be a manifold satisfying certain conditions which are weaker than those of E. Thomas[12], andf:M→N be a map with codimension one or two. We give necessary and sufficient conditions forf to be homotopic to a map with maximal rank. As an application, we completely determine the codimension one or two immersions
of Dold manifolds in real projective spaces. 相似文献
11.
Changyu Xia 《Compositio Mathematica》2002,132(1):49-55
In this paper, we use the theory of critical points of distance functions to study the rigidity and topology of Riemannian manifolds with sectional curvature bounded below. We prove that an n-dimensional complete connected Riemannian manifold M with sectional curvature K
M
1 is isometric to an n-dimensional Euclidean unit sphere if M has conjugate radius bigger than /2 and contains a geodesic loop of length 2. We also prove that if M is an n(3)-dimensional complete connected Riemannian manifold with K
M
1 and radius bigger than /2, then any closed connected totally geodesic submanifold of dimension not less than two of M is homeomorphic to a sphere. 相似文献
12.
In this article, we study topology of complete non‐compact Riemannian manifolds. We show that a complete open manifold with quadratic curvature decay is diffeomorphic to a Euclidean n ‐space ?n if it contains enough rays starting from the base point. We also show that a complete non‐compact n ‐dimensional Riemannian manifold M with nonnegative Ricci curvature and quadratic curvature decay is diffeomorphic to ?n if the volumes of geodesic balls in M grow properly. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Duane Randall 《manuscripta mathematica》1990,69(1):339-351
LetM
n
denote any closed connected CAT manifold of positive dimensionn. We define CATs(Mn) to be the smallest positive dimension of all closed connected CAT manifoldsN for which the CAT span ofM×N is strictly greater than the CAT span ofN. We determine a formula for this characteristic number which involves only the Kirby-Siebenmann numberks(M) ofM and a Stiefel-Whitney number. Several results on splitting the tangent bundles of closed 4-manifolds are obtained. For example,
both the Euler number ofM
4 andks(M4) represent the total obstruction to positive CAT span for a non-smoothable closed connected 4-manifold.
Dedicated to the memory of Professor Otto Endler 相似文献
14.
The most successful known algorithms enumerating the elementary cycles of a directed graph are based on a backtracking strategy. Such existing algorithms are discussed and a new backtracking algorithm is proposed which is bounded byO(N +M(C + 1)) time, for a directed graph withN vertices,M edges andC elementary cycles.Research supported by the Conselho National de Desenvolvimento Científico e Tecnológico — CNPq — Brasil. 相似文献
15.
In this paper we will present upper bounds for the length of a shortest closed geodesic on a manifold M diffeomorphic to the standard two-dimensional sphere. The first result is that the length of a shortest closed geodesic l(M) is bounded from above by 4r , where r is the radius of M . (In particular that means that l(M) is bounded from above by 2d, when M can be covered by a ball of radius d/2, where d is the diameter of M.) The second result is that l(M) is bounded from above by 2( max{r1,r2}+r1+r2), when M can be covered by two closed metric balls of radii r1,r2 respectively. For example, if r1 = r2= d/2 , thenl(M) 3d. The third result is that l(M) 2(max{r1,r2r3}+r1+r2+r3), when M can be covered by three closed metric balls of radii r1,r2,r3. Finally, we present an estimate for l(M) in terms of radii of k metric balls covering M, where k 3, when these balls have a special configuration. 相似文献
16.
A. V. Isaev 《Journal of Geometric Analysis》2008,18(3):795-799
We prove a characterization theorem for the unit polydisc Δ
n
⊂ℂ
n
in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δ
n
) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δ
n
.
相似文献
17.
Let V
n
be an open manifold of non-negative sectional curvature with a soul Σ of co-dimension two. The universal cover of the unit normal bundle N of the soul in such a manifold is isometric to the direct product M
n-2 × R. In the study of the metric structure of V
n
an important role plays the vector field X which belongs to the projection of the vertical planes distribution of the Riemannian submersion on the factor M in this metric splitting . The case n = 4 was considered in [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127–136 (2003)] where the authors prove that X is a Killing vector field while the manifold V
4 is isometric to the quotient of by the flow along the corresponding Killing field. Following an approach of [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127–136 (2003)] we consider the next case n = 5 and obtain the same result under the assumption that the set of zeros of X is not empty. Under this assumption we prove that both M
3 and Σ3 admit an open-book decomposition with a bending which is a closed geodesic and pages which are totally geodesic two-spheres,
the vector field X is Killing, while the whole manifold V
5 is isometric to the quotient of by the flow along corresponding Killing field.
Supported by the Faculty of Natural Sciences of the Hogskolan i Kalmar (Sweden). 相似文献
18.
Xu Cheng 《Mathematische Annalen》2003,325(2):229-248
Let M be a 2m-dimensional compact Riemannian manifold with Anosov geodesic flow. We prove that every closed bounded k form, k≥2, on the universal covering of M is d(bounded). Further, if M is homotopy equivalent to a compact K?hler manifold, then its Euler number χ(M) satisfies (−1)
m
χ(M)>0.
Received: 25 September 2001 / Published Online: 16 October 2002 相似文献
19.
We prove that given a simply connected compact manifold M and a
closed manifold N, any map in the Sobolev space W
1,2(M,N) can be
approximated weakly by smooth maps between M and N.
Submitted: September 2002, Final version: November 2002. 相似文献
20.
Fumio Narita 《Geometriae Dedicata》1997,65(1):103-116
The main results of this paper are as follows. (a) Let : M N be a non-trivial Riemannian submersion with totally geodesic fibers of dimension 1 over an Einstein manifold N. If M is compact and admits a standard Einstein--Weyl structure with constant Einstein--Weyl function, then N admits a Kähler structure andM a Sasakian structure. (b) Let
be a Riemannian submersion with totally geodesic fibers and N an Einstein manifold of positive scalar curvature
. If M admits a standard Sasakian structure, then M admits an Einstein--Weyl structure with constant Einstein--Weyl function. 相似文献