Positive manifold

The Ricci ﬂow was introduced by Hamilton in 1982 [H1] in order to prove that a compact threemanifold admitting a Riemannian metric of positive Ricci curvature is a spherical space form. In dimension four Hamilton showed that compact fourmanifolds with positive curvature operators are spherical space forms as well [H2]. More generally, the same conclusion holds for compact fourmanifolds with 2positive curvature operators [Che]. Recall that a curvature operator is called 2positive, if the sum of its two smallest eigenvalues is positive. ...
20p dontetvui 17012013 26 7 Download

There are very few examples of Riemannian manifolds with positive sectional curvature known. In fact in dimensions above 24 all known examples are diﬀeomorphic to locally rank one symmetric spaces. We give a partial explanation of this phenomenon by showing that a positively curved, simply connected, compact manifold (M, g) is up to homotopy given by a rank one symmetric space, provided that its isometry group Iso(M, g) is large. More precisely we prove ﬁrst that if dim(Iso(M, g)) ≥ 2 dim(M ) − 6, then M is tangentially homotopically equivalent to a rank one symmetric space or M...
63p noel_noel 17012013 26 4 Download

HUMAN PERFORMANCE: Role of General Mental Ability in Industrial, Work, and Organizational Psychology
Individual differences that have consequences for work behaviors (e.g., job performance) are of great concern for organizations, both public and private. General mental ability has been a popular, although much debated, construct in Industrial, Work, and Organizational (IWO) Psychology for almost 100 years. Individuals differ on their endowments of a critical variable—intelligence—and differences on this variable have consequences for life outcomes.
232p cronus75 13012013 36 6 Download

The goal of this work is to give a precise numerical description of the K¨hler cone of a compact K¨hler manifold. Our main result states that the a a K¨hler cone depends only on the intersection form of the cohomology ring, the a Hodge structure and the homology classes of analytic cycles: if X is a compact K¨hler manifold, the K¨hler cone K of X is one of the connected components of a a the set P of real (1, 1)cohomology classes {α} which are numerically positive on analytic cycles, i.e. Y αp 0 for every irreducible analytic...
29p tuanloccuoi 04012013 23 5 Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Positively Curved Combinatorial 3Manifolds...
23p thulanh7 04102011 15 2 Download

Inspired by Lorenz’ remarkable chaotic ﬂow, we describe in this paper the structure of all C 1 robust transitive sets with singularities for ﬂows on closed 3manifolds: they are partially hyperbolic with volumeexpanding central direction, and are either attractors or repellers. In particular, any C 1 robust attractor with singularities for ﬂows on closed 3manifolds always has an invariant foliation whose leaves are forward contracted by the ﬂow, and has positive Lyapunov exponent at every orbit, showing that any C 1 robust attractor resembles a geometric Lorenz attractor. ...
59p tuanloccuoi 04012013 28 6 Download

We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature – in fact, we only assume that the geodesic ﬂow has the Anosov property. In the semiclassical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1.
43p dontetvui 17012013 22 6 Download

We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G˚ ardingGindikin fractional integrals associated to the cone of positive deﬁnite matrices. By using this connection, we obtain Abeltype representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces.
36p tuanloccuoi 04012013 25 5 Download

Exponential decay of correlations for C 4 contact Anosov ﬂows is established. This implies, in particular, exponential decay of correlations for all smooth geodesic ﬂows in strictly negative curvature. 1. Introduction The study of decay of correlations for hyperbolic systems goes back to the work of Sinai [36] and Ruelle [32]. While many results were obtained through the years for maps, some positive results have been established for Anosov ﬂows only recently.
39p tuanloccuoi 04012013 28 5 Download

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric. 1. Introduction Let (M n , g) be a smooth, closed Riemannian manifold of dimension n.
58p noel_noel 17012013 30 5 Download

Let g be a scattering metric on a compact manifold X with boundary, i.e., a smooth metric giving the interior X ◦ the structure of a complete Riemannian manifold with asymptotically conic ends. An example is any compactly supported perturbation of the standard metric on Rn . Consider the operator H = 1 ∆ + V , where ∆ is the positive Laplacian with respect to g and V is a 2 smooth realvalued function on X vanishing to second order at ∂X. Assuming that g is nontrapping, we construct a global parametrix U(z, w, t) for the kernel...
38p noel_noel 17012013 24 4 Download

One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (e.g. energy, position, momentum, etc.
239p thienbinh1311 13122012 23 3 Download