共查询到20条相似文献,搜索用时 31 毫秒
1.
Dominic Wright 《Selecta Mathematica, New Series》2011,17(2):281-299
We prove that any asymptotically locally Euclidean scalar-flat K?hler 4-orbifold whose isometry group contains a 2-torus is
isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k−1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic
whose isometry group contains a 2-torus is conformally equivalent, up to an orbifold covering, to a quaternionic quotient of k-dimensional quaternionic projective space by a (k − 1)-torus. 相似文献
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3.
Oliver Baues 《Geometriae Dedicata》1999,75(1):33-56
Affine structures on surfaces are constructed by gluing polygons. The geometry of the affine surface depends on the shape of the polygon(s) and the particular gluing transformations used. The affine version of the Poincaré fundamental polygon theorem expresses the fundamental group and holonomy of the surface in terms of the gluing data. The theorem may be used to construct all complete affine structures on the 2-torus. The space of inequivalent holonomy representations of such structures is homeomorphic to R2. 相似文献
4.
We confirm the Halperin-Carlsson conjecture for free Z_p-torus actions(p is a prime) on 2-dimensional finite CW-complexes and free Z_2-torus actions on closed 3-manifolds. 相似文献
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6.
We study the action-minimizing half-orbits of an area-preserving monotone twist map of an annulus. We show that these so-called rays are always asymptotic to action-minimizing orbits. In the spirit of Aubry-Mather theory which analyses the set of action-minimizing orbits we investigate existence and properties of rays. By analogy with the geometry of the geodesics on a Riemannian 2-torus we define a Busemann function for every ray. We use this concept to prove that the minimal average action A() is differentiable at irrational rotation numbers while it is generically non-differentiable at rational rotation numbers (cf. also [18]). As an application of our results in the geometric framework we prove that a Riemannian 2-torus which has the same marked length spectrum as a flat 2-torus is actually isometric to this flat torus. 相似文献
7.
Marko Stoši? 《Topology and its Applications》2009,156(3):533-541
In this paper we show that there is a cut-off in the Khovanov homology of (2k,2kn)-torus links, namely that the maximal homological degree of non-zero homology groups of (2k,2kn)-torus links is 2k2n. Furthermore, we calculate explicitly the homology group in homological degree 2k2n and prove that it coincides with the center of the ring Hk of crossingless matchings, introduced by M. Khovanov in [M. Khovanov, A functor-valued invariant for tangles, Algebr. Geom. Topol. 2 (2002) 665-741, arXiv:math.QA/0103190]. This gives the proof of part of a conjecture by M. Khovanov and L. Rozansky in [M. Khovanov, L. Rozansky, A homology theory for links in S2×S1, in preparation]. Also we give an explicit formula for the ranks of the homology groups of (3,n)-torus knots for every n∈N. 相似文献
8.
Journal of Fourier Analysis and Applications - For the noncommutative 2-torus, we define and study Fourier transforms arising from representations of states with central supports in the bidual,... 相似文献
9.
Dominic Wright 《Selecta Mathematica, New Series》2011,17(2):223-280
We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic.
Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines
induces meromorphic data, which we use to recover the conformal structure. A compact anti-self-dual orbifold can also be constructed
by adding a point at infinity to an asymptotically locally Euclidean (ALE) scalar-flat K?hler orbifold. We use this observation
to classify ALE scalar-flat K?hler 4-orbifolds whose isometry group contain a 2-torus. 相似文献
10.
Acta Mathematica Sinica, English Series - We prove the Möbius disjointness conjecture in short intervals for a class of skew products on the 2-torus, which includes Furstenberg’s example... 相似文献
11.
Misha Bialy 《Geometric And Functional Analysis》2010,20(2):357-367
We propose a new condition à{{\aleph}} which enables us to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first,
we strengthen Kozlov’s theorem on non-integrability on surfaces of higher genus. In the second, we study integrable geodesic
flows on a 2-torus. Our main result for a 2-torus describes the phase portraits of integrable flows. We prove that they are
essentially standard outside what we call separatrix chains. The complement to the union of the separatrix chains is C
0-foliated by invariant sections of the bundle. 相似文献
12.
V. I. Arnold 《Proceedings of the Steklov Institute of Mathematics》2007,258(1):3-12
Trigonometric polynomials on the 2-torus that belong to a special six-parameter family are classified up to diffeomorphisms of the image and the preimage that are homotopic to the identity. 相似文献
13.
We show solvability of the systems of equations modeled on certain spines of 3-manifolds. We extend a result by Duncan and Howie about the 2-skeleton of the 3-torus. 相似文献
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V. A. Sharafutdinov 《Siberian Mathematical Journal》2016,57(1):155-173
A symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative equals zero. There is a one-to-one correspondence between Killing tensor fields and first integrals of the geodesic flow which depend polynomially on the velocity. Therefore Killing tensor fields relate closely to the problem of integrability of geodesic flows. In particular, the following question is still open: does there exist a Riemannian metric on the 2-torus which admits an irreducible Killing tensor field of rank ≥ 3? We obtain two necessary conditions on a Riemannian metric on the 2-torus for the existence of Killing tensor fields. The first condition is valid for Killing tensor fields of arbitrary rank and relates to closed geodesics. The second condition is obtained for rank 3 Killing tensor fields and pertains to isolines of the Gaussian curvature. 相似文献
16.
R. Pacheco 《Differential Geometry and its Applications》2009,27(3):352-361
In this paper we prove that, in contrast with the Sn and CPn cases, there are harmonic 2-tori into the quaternionic projective space HPn which are neither of finite type nor of finite uniton number; we also prove that any harmonic 2-torus in a compact Riemannian symmetric space which can be obtained via the twistor construction is of finite type if and only it is constant; in particular, we conclude that any harmonic 2-torus in CPn or Sn which is simultaneously of finite type and of finite uniton number must be constant. 相似文献
17.
In this paper we prove that a compact oriented hypersurface of a Euclidean
sphere with nonnegative Ricci curvature and infinite fundamental group is isometric
to an H(r)-torus
with constant mean curvature. Furthermore, we generalize, whithout any
hypothesis about the mean curvature, a characterization of Clifford torus due to
Hasanis and Vlachos.
Received: 19 March 2002 相似文献
18.
Richard Swanson Russell Walker 《Proceedings of the American Mathematical Society》1996,124(10):3247-3255
We construct a diffeomorphism of the 3-torus whose rotation set is not closed. We prove that the rotation set of a homeomorphism of the -torus contains the extreme points of its closed convex hull. Finally, we show that each pseudo-rotation set is closed for torus homeomorphisms.
19.
We show that certain derived-from-Anosov diffeomorphisms on the 2-torus may be realized as the dynamics on a center-stable or center-unstable torus of a 3-dimensional strongly partially hyperbolic system. We also construct examples of center-stable and center-unstable tori in higher dimensions. 相似文献
20.
Using basic harmonic analysis on the n-torus, it is shown thatthe non-commutative n-tori are the only primitive C*-algebras(up to isomorphism) on which the n-torus Tn acts freely andergodically. An explicit construction recovers the generatingunitaries in a natural way from the action. 2000 MathematicsSubject Classification 46L55. 相似文献