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1.
Let γ be a hyperbolic closed orbit of a C~1 vector field X on a compact C~∞ manifold M of dimension n≥3,and let HX(γ)be the homoclinic class of X containingγ.In this paper,we prove that C~1-generically,if HX(γ)is expansive and isolated,then it is hyperbolic.  相似文献   

2.
Canonical Foliations of Certain Classes of Almost Contact Metric Structures   总被引:1,自引:0,他引:1  
The purpose of this paper is to study the canonical foliations of an almost cosymplectic or almost Kenmotsu manifold M in a unified way. We prove that the canonical foliation F defined by the contact distribution is Riemannian and tangentially almost Kahler of codimension 1 and that F is tangentially Kahler if the manifold M is normal. Furthermore, we show that a semi-invariant submanifold N of such a manifold M admits a canonical foliation FN which is defined by the antiinvariant distribution and a canonical cohomology class c(N) generated by a transversal volume form for FN. In addition, we investigate the conditions when the even-dimensional cohomology classes of N are non-trivial. Finally, we compute the Godbillon Vey class for FN.  相似文献   

3.
Let M be a smooth manifold with Finsler metric F,and let T M be the slit tangent bundle of M with a generalized Riemannian metric G,which is induced by F.In this paper,we prove that (i) (M,F) is a Landsberg manifold if and only if the vertical foliation F V is totally geodesic in (T M,G);(ii) letting a:= a(τ) be a positive function of τ=F 2 and k,c be two positive numbers such that c=2 k(1+a),then (M,F) is of constant curvature k if and only if the restriction of G on the c-indicatrix bundle IM (c) is bundle-like for the horizontal Liouville foliation on IM (c),if and only if the horizontal Liouville vector field is a Killing vector field on (IM (c),G),if and only if the curvature-angular form Λ of (M,F) satisfies Λ=1-a 2/R on IM (c).  相似文献   

4.
Suppose Mi = Vi ∪ Wi (i = 1,2) are Heegaard splittings. A homeomorphism f : F1 → F2 produces an attached manifold M = M1 ∪F1=F2 M2, where Fi ∪→ δ_Wi. In this paper we define a surface sum of Heegaard splittings induced from the Heegaard splittings of M1 and M2, and give a sufficient condition when the surface sum of Heegaard splitting is stabilized. We also give examples showing that the surface sum of Heegaard splittings can be unstabilized. This indicates that the surface sum of Heegaard splittings and the amalgamation of Heegaard splittings can give different Heegaard structures.  相似文献   

5.
We determine a 2-codimensional para-CR structure on the slit tangent bundle T0 M of a Finsler manifold(M,F) by imposing a condition regarding the almost paracomplex structure P associated to F when restricted to the structural distribution of a framed para-f-structure.This condition is satisfied when(M,F) is of scalar flag curvature(particularly constant) or if the Riemannian manifold(M,g) is of constant curvature.  相似文献   

6.
In this paper, we study (α,β)-metrics of scalar flag curvature on a manifold M of dimension n (n 〉 3). Suppose that an (α,β)-metric F is not a Finsler metric of Randers type, that is, F ≠k1 V√α^2 + k2β^2 + k3β, where k1 〉 0, k2 and k3 are scalar functions on M. We prove that F is of scalar flag curvature and of vanishing S-curvature if metric. In this case, F is a locally Minkowski and only if the flag curvature K = 0 and F is a Berwald metric.  相似文献   

7.
Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the flag curvature is constant.  相似文献   

8.
《数学季刊》1995,10(2):40-44
Given a projective map F:M→N of a complete Riemannian manifold to a Riemannian manifold with the sectional curvature bounded above by a negative constant,we prove that f decreases volume up to a constant depending only on the curvatures of M and N.This generalizes the result due to Har‘el.  相似文献   

9.
Let (M, ω) be a closed symplectic 2n-dimensional manifold. Donaldson in his paper showed that there exist 2m-dimensional symplectie submanifolds (V^2m,ω) of (M,ω), 1 ≤m ≤ n - 1, with (m - 1)-equivalent inclusions. On the basis of this fact we obtain isomorphic relations between kernel of Lefschetz map of M and kernels of Lefschetz maps of Donaldson submanifolds V^2m, 2 ≤ m ≤ n - 1. Then, using this relation, we show that the flux group of M is discrete if the action of π1 (M) on π2(M) is trivial and there exists a retraction r : M→ V, where V is a 4-dimensional Donaldson submanifold. And, in the symplectically aspherical case, we investigate the flux groups of the manifolds.  相似文献   

10.
Given a C~2-function f on a Hilbedrt Riemannian manifold M, let ∑ be a. nondegonerate critical manifold of f, what becomes of ∑, if we perturbe f to f+g? When g is a C~2 perturbation, i.e. ||g||c~2 is small, there was a result due to M. Reeken by the inverse function theorem. It was rediscovered by Ambrosetti et.  相似文献   

11.
Let M be a simple 3-manifold such that one component of ∂M, say F, has genus at least two. For a slope α on F, we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F. If M(α) is reducible, then α is called a reducing slope. In this paper, we shall prove that the distance between two separating, reducing slopes on F is at most 4. This work is supported by NSFC (10625102).  相似文献   

12.
We investigate the validity of the isometry extension property for (Riemannian) Einstein metrics on compact manifolds M with boundary ∂M. Given a metric γ on ∂M, this is the issue of whether any Killing field X of (∂M, γ) extends to a Killing field of any Einstein metric (M, g) bounding (∂M, γ). Under a mild condition on the fundamental group, this is proved to be the case at least when X preserves the mean curvature of ∂M in (M, g).  相似文献   

13.
In this note, we give the L^p (1 〈 p 〈∞) boundedness of the parabolic Littlewood Paley g-function with rough kernel.  相似文献   

14.
Circularm-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifoldM 4 with boundary ∂M 4 that satisfies the condition ξ(∂M 4)=ξ(M 4,∂M 4)=0 but does not contain any circularm-function. We prove that a manifold with boundaryM n (n≥5) such that ξ(∂M n , ∂M n )=0 always contains a circularm-function without critical points in the interior manifold. Sukhumi Branch of the Tbilisi University, Sukhumi. Translated from Ukrainskii Matermaticheskii Zhurnal, Vol. 46, No. 6, pp. 776–781, June, 1994.  相似文献   

15.
For a complete Riemannian manifold M with compact boundary ∂M denote by $\Cut$ the cut locus of $\f M$ in M. The rolling radius of M is roll(M)≔ dist(∂M, ? M ). Let Focal(∂M) be the focal distance of ∂M in M. Then conditions are given that imply the equality roll(M)= Focal(∂M). This generalizes Blaschke's rolling theorem from bounded convex domains in Euclidean space to more general Euclidean domains and to Riemannian manifolds with boundary. Received: 28 August 1998 / Revised version: 8 February 1999  相似文献   

16.
We show that a non-Sasakian contact metric manifold with η-parallel torsion tensor and sectional curvatures of plane sections containing the Reeb vector field different from 1 at some point, is a (kμ)-contact manifold. In particular for the standard contact metric structure of the tangent sphere bundle the torsion tensor is η-parallel if and only if M is of constant curvature, in which case its associated pseudo-Hermitian structure is CR- integrable. Next we show that if the metric of a non-Sasakian (k, μ)-contact manifold (M, g) is a gradient Ricci soliton, then (M, g) is locally flat in dimension 3, and locally isometric to E n+1 × S n (4) in higher dimensions.   相似文献   

17.
LetM be a σ-finite von Neumann algebra andα be an action ofR onM. LetH (α) be the associated analytic subalgebra; i.e.H (α)={XM: sp(X) [0, ∞]}. We prove that every σ-weakly closed subalgebra ofM that containsH (α) isH (γ) for some actionγ ofR onM. Also we show that (assumingZ(M)∩M α = Ci)H (α) is a maximal σ-weakly closed subalgebra ofM if and only if eitherH (α)={AM: (I−F)xF=0} for some projectionFM, or sp(α)=Γ(α).  相似文献   

18.
We consider random systems generated by two-sided compositions of random surface diffeomorphisms,together with an ergodic Borel probability measure μ.Let D(μω)be its dimension of the sample measure,then we prove a formula relating D(μω)to the entropy and Lyapunov exponents of the random system,where D(μω)is dimHμω,-/dinBμω,or-/dimBμω.  相似文献   

19.
Many known distance-regular graphs have extra combinatorial regularities: One of them is t-homogeneity. A bipartite or almost bipartite distance-regular graph is 2-homogeneous if the number γ i  = |{x | ∂(u, x) = ∂(v, x) = 1 and ∂(w, x) = i − 1}| (i = 2, 3,..., d) depends only on i whenever ∂(u, v) = 2 and ∂(u, w) = ∂(v, w) = i. K. Nomura gave a complete classification of bipartite and almost bipartite 2-homogeneous distance-regular graphs. In this paper, we generalize Nomura’s results by classifying 2-homogeneous triangle-free distance-regular graphs. As an application, we show that if Γ is a distance-regular graph of diameter at least four such that all quadrangles are completely regular then Γ is isomorphic to a binary Hamming graph, the folded graph of a binary Hamming graph or the coset graph of the extended binary Golay code of valency 24. We also consider the case Γ is a parallelogram-free distance-regular graph. This research was partially supported by the Grant-in-Aid for Scientific Research (No.17540039), Japan Society of the Promotion of Science.  相似文献   

20.
Let M be a smooth connected orientable compact surface and let Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) be a space of all Morse functions f : MS 1 without critical points on ∂M such that, for any connected component V of ∂M, the restriction f : VS 1 is either a constant map or a covering map. The space Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) is endowed with the C -topology. We present the classification of connected components of the space Fcov ( M,S1 ) {\mathcal{F}_{{\rm cov} }}\left( {M,{S^1}} \right) . This result generalizes the results obtained by Matveev, Sharko, and the author for the case of Morse functions locally constant on ∂M.  相似文献   

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