Riemannian metric

(BQ) Ebook Mathematical methods of classical mechanics (Second edition): Part 2 presents the following content: Riemannian curvature; geodesics of left-invariant metrics on lie groups and the hydrodynamics of ideal fluids; symplectic structures on algebraic manifolds; contact structures; dynamical systems with symmetries; normal forms of quadratic hamiltonians; normal forms of hamiltonian systems near stationary points and closed trajectories; theory of perturbations of conditionally periodic motion, and kolmogorov's theorem;....

219p runordie6 10-08-2022 11 2   Download

In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that this is obtained if the total space is an b-almost Kenmotsu manifold.

11p danhdanh27 07-01-2019 15 2   Download

In the context of Riemannian geometry, the tangent bundle TM of a Riemannian manifold (M, g) was classically equipped with the Sasaki metric gS , which was introduced in 1958 by Sasaki. In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.

12p danhdanh27 07-01-2019 19 1   Download

In this paper, we characterize the pointwise slant submersions from cosymplectic manifolds onto Riemannian manifolds and give several examples.

12p danhdanh27 07-01-2019 16 2   Download

We introduce radical anti-invariant lightlike submanifolds of a semi Riemannian product manifold and give examples. After we obtain the conditions of integrability of distributions which are involved in the definition of radical anti-invariant lightlike submanifolds, we investigate the geometry of leaves of distributions.

21p danhdanh27 07-01-2019 21 1   Download

In Cheeger and Gromoll study complete manifolds of nonnegative curvature and suggest a construction of Riemannian metrics useful in that contex. The main purpose of the paper is to investigate geodesics on the tangent bundle with respect to the Cheeger-Gromoll metric.

7p danhdanh27 07-01-2019 20 1   Download

In this paper, we consider Finsler metrics defined by a Riemannian metric and a 1-form on a manifold. We these metrics with vanishing S-curvature. We find some conditions under which such a Finsler metric is Berwaldian or locally Minkowskian.

12p tuongvidanh 06-01-2019 16 1   Download

In this paper, we first define the concept of paracontact semi-Riemannian submersions between almost paracontact metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost paracontact structure of the total manifold.

15p tuongvidanh 06-01-2019 17 2   Download

The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. We discuss the problem of integrability for Golden Riemannian structures by using a φ-operator which is applied to pure tensor fields.

11p tuongvidanh 06-01-2019 18 1   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 semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics. 1. Introduction, statement of results We consider a compact Riemannian manifold M of dimension d ≥ 2, and assume that the geodesic flow (g t )t∈R , acting on the unit tangent bundle of M , has a “chaotic”...

43p dontetvui 17-01-2013 49 7   Download

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

20p dontetvui 17-01-2013 49 7   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 17-01-2013 52 6   Download

This paper is a continuation of Fefferman’s program [7] for studying the geometry and analysis of strictly pseudoconvex domains. The key idea of the program is to consider the Bergman and Szeg¨ kernels of the domains as o analogs of the heat kernel of Riemannian manifolds. In Riemannian (or conformal) geometry, the coefficients of the asymptotic expansion of the heat kernel can be expressed in terms of the curvature of the metric; by integrating the coefficients one obtains index theorems in various settings. ...

18p noel_noel 17-01-2013 48 5   Download

We study “flat knot types” of geodesics on compact surfaces M 2 . For every flat knot type and any Riemannian metric g we introduce a Conley index associated with the curve shortening flow on the space of immersed curves on M 2 . We conclude existence of closed geodesics with prescribed flat knot types, provided the associated Conley index is nontrivial. 1. Introduction If M is a surface with a Riemannian metric g then closed geodesics on (M, g) are critical points of the length functional L(γ) = |γ (x)|dx defined on the space of unparametrized C...

56p noel_noel 17-01-2013 58 9   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 real-valued 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 17-01-2013 42 5   Download

We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction. 1. Introduction and statement of the results Let (M, g) be a compact Riemannian manifold with boundary ∂M . Let dg (x, y) denote the geodesic distance between x and y. The inverse problem we address in this paper is whether we can determine the Riemannian metric g knowing dg (x, y) for any x ∈ ∂M , y ∈ ∂M . ...

19p noel_noel 17-01-2013 41 3   Download

This paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R3 (with the flat metric). This study is undertaken here and completed in [CM6]. These local results are then applied in [CM7] where we describe the general structure of fixed genus surfaces in 3-manifolds. There are two local models for...

43p tuanloccuoi 04-01-2013 67 7   Download

For each k ∈ Z, we construct a uniformly contractible metric on Euclidean space which is not mod k hypereuclidean. We also construct a pair of uniformly contractible Riemannian metrics on Rn , n ≥ 11, so that the resulting manifolds Z and Z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism. We show that for these lf spaces the C ∗ -algebra assembly map K∗ (Z) → K∗ (C ∗ (Z)) from locally finite K-homology to the K-theory of the bounded propagation algebra is not a monomorphism ...

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Institute for Theoretical Physics University of California Santa Barbara, CA 93106 carroll@itp.ucsb.edu December 1997 Abstract These notes represent approximately one semester’s worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein’s equations, and three applications: gravitational radiation, black holes, and cosmology. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/notes/. NSF-ITP/97-147 gr-qc/9712019 .i Table of Contents 0.

238p possibletb 23-11-2012 66 8   Download