共查询到20条相似文献,搜索用时 312 毫秒
1.
Yoshinobu Kamishima 《Central European Journal of Mathematics》2014,12(6):861-878
We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type. 相似文献
2.
Yu. M. Ustinovsky 《Proceedings of the Steklov Institute of Mathematics》2014,286(1):198-208
We study the geometry of compact complex manifolds M equipped with a maximal action of a torus T = (S 1) k . We present two equivalent constructions that allow one to build any such manifold on the basis of special combinatorial data given by a simplicial fan Σ and a complex subgroup H ? T ? = (?*) k . On every manifold M we define a canonical holomorphic foliation F and, under additional restrictions on the combinatorial data, construct a transverse Kähler form ω F . As an application of these constructions, we extend some results on the geometry of moment-angle manifolds to the case of manifolds M. 相似文献
3.
Alan Weinstein 《Journal of the European Mathematical Society》2000,2(1):53-86
We define a C
1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C
1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure
combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds
as zeros of sections of extended normal bundles.
Received September 14, 1999 / final version received November 29, 1999 相似文献
4.
Grzegorz Graff Agnieszka Kaczkowska Piotr Nowak-Przygodzki Justyna Signerska 《Topology and its Applications》2012,159(10-11):2728-2735
Let f be a self-map of a compact connected manifold M. We characterize Lefschetz periodic point free continuous self-maps of M for several classes of manifolds and generalize the results of Guirao and Llibre [J.L.G. Guirao, J. Llibre, On the Lefschetz periodic point free continuous self-maps on connected compact manifolds, Topology Appl. 158 (16) (2011) 2165–2169]. 相似文献
5.
6.
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics C n which are invariant with respect to the natural action of the real torus (S 1) n onto C n . The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope. Finally, as a nice consequence, we obtain that affine non-Kähler compact complex manifolds can have arbitrary amount of torsion in their homology groups, contrasting with the Kähler situation. 相似文献
7.
Let G be a compact Lie group acting isometrically on a compact Riemannian manifold M with nonempty fixed point set M
G
. We say that M is fixed-point homogeneous if G acts transitively on a normal sphere to some component of M
G
. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify nonnegatively
curved fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected
4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure. 相似文献
8.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(4):465-470
Let M be a compact -analytic surface, let Γ ⊂ M be a compact analytic subvariety, and let X := Mx00393;. We are interested in the following two problems: Assume that X does not contain any compact curve and that Γ is an irreducible compact curve such that Γ2 ≥ 0 (resp. assume that the analytic cohomology groups H1 (X, Ωp) = 0, for all 0 ≤ p ≤ 2). Is X always Stein? It is our main purpose here to provide an affirmative answer to those two problems, provided M is either a (minimal) ruled surface or a non-algebraic compact surface. Also, the affine structure of such Stein surfaces will be discussed. 相似文献
9.
We prove that compact quaternionic-Kähler manifolds of positive scalar curvature admit no almost complex structure, even in the weak sense, except for the complex Grassmannians Gr2(?n+2). We also prove that irreducible inner symmetric spaces M 4n of compact type are not weakly complex, except for spheres and Hermitian symmetric spaces. 相似文献
10.
HEMANGI M SHAH 《Proceedings Mathematical Sciences》2014,124(3):419-425
In this note we reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger–Gromov splitting theorem. We also confirm that if a harmonic manifold M has same volume density function as ? n , then M is flat. 相似文献
11.
A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin’s and Gualtieri’s generalized complex geometry, (4,4)-manifolds are called “generalized hyperkähler manifolds”. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure. 相似文献
12.
In this paper, for closed connected oriented manifolds M and N of the same dimension, we study the degree of a triple (??, p, q), where p is a Vietoris map from a compact space ?? to M and q is a continuous map from ?? to N. In particular, we have Borsuk?CUlam-type degree theorems on manifolds with involutions. 相似文献
13.
Tedi Dr?ghici 《Differential Geometry and its Applications》2005,22(2):147-158
It is shown that the existence of an ω-compatible Einstein metric on a compact symplectic manifold (M,ω) imposes certain restrictions on the symplectic Chern numbers. Examples of symplectic manifolds which do not satisfy these restrictions are given. The results offer partial support to a conjecture of Goldberg. 相似文献
14.
Abdênago Barros Ernani Ribeiro Jr 《Bulletin of the Brazilian Mathematical Society》2014,45(2):325-341
The aim of this paper is to present some structural equations for generalized m-quasi-Einstein metrics (M n , g, ? f, λ), which was defined recently by Catino in [11]. In addition, supposing that M n is an Einstein manifold we shall show that it is a space form with a well defined potential f. Finally, we shall derive a formula for the Laplacian of its scalar curvature which will give some integral formulae for such a class of compact manifolds that permit to obtain some rigidity results. 相似文献
15.
In this paper we prove a global existence result for nonlinear Klein-Gordon equations in infinite homogeneous waveguides, R×M, with smooth small data, where M=(M,g) is a Zoll manifold, or a compact revolution hypersurface. The method is based on normal forms, eigenfunction expansion and the special distribution of eigenvalues of the Laplace-Beltrami on such manifolds. 相似文献
16.
In this paper we establish the best constants for a Sobolev inequality and a Sobolev trace inequality on compact Riemannian manifolds with boundary, the functions being invariant under the action of a compact subgroup G of the isometry group I(M,g) and we give applications to some nonlinear PDEs with upper critical Sobolev exponent. 相似文献
17.
18.
Danny Fundinger 《Journal of Nonlinear Science》2008,18(4):391-413
This paper presents a new numerical method for computing global stable manifolds and global stable sets of nonlinear discrete
dynamical systems. For a given map f:ℝ
d
→ℝ
d
, the proposed method is capable of yielding large parts of stable manifolds and sets within a certain compact region M⊂ℝ
d
. The algorithm divides the region M in sets and uses an adaptive subdivision technique to approximate an outer covering of the manifolds. In contrast to similar
approaches, the method requires neither the system’s inverse nor its Jacobian. Hence, it can also be applied to noninvertible
and piecewise-smooth maps. The successful application of the method is illustrated by computation of one- and two-dimensional
stable manifolds and global stable sets. 相似文献
19.
Abstract. Let M be a complete nondegenerate locally standard CR manifold. We show that a necessary and sufficient condition for M to be compact is that the Lie algebra of its infinitesimal CR automorphisms is semisimple. In general we realize M as a Mostow fibration over a compact CR manifoldB whose universal covering is a Cartesian product of Hermitian symmetric spaces and compact nondegenerate standard CR manifolds.
Received: 22 July 1998 / Published online: 8 May 2000 相似文献
20.
We prove a Harnack-type inequality inf|S|/sup|S|>1?ε(W, M, V) satisfied by the sections of a Riemannian vector bundleW lying in the kernel of a Schrödinger operator ∨*∨+V underL p -pinching assumptions on the potentialV and derive various topological and geometric consequences. For instance, we prove a fibration theorem which gives a classification of almost non-negatively curved compact manifolds by the first Betti number. In the case of almost non-positively curved compact manifolds, we prove that the minimal volume must vanish whenever the isometry group is not finite and give conditions implying that it is abelian. 相似文献