Geodesic curvature

Part 2 of ebook "Multivariate calculus and geometry (Third edition)" provides readers with contents including: Chapter 11 - Surface area; Chapter 12 - Surface integrals; Chapter 13 - Stokes' theorem; Chapter 14 - Triple integrals; Chapter 15 - The divergence theorem; Chapter 16 - Geometry of surfaces in R3; Chapter 17 - Gaussian curvature; Chapter 18 - Geodesic curvature;...

130p daonhiennhien 03-07-2024 1 1   Download

Ebook Complex Analysis and Differential Geometry: Part 2 presents the following content: Tensor Fields in Curvilinear Coordinates; New Spherical Indicatrices and their Characterizations; Developable Surface Fitting to Point Clouds; Local Intrinsic Geometry of Surfaces; Geodesic Curvature and Christoffel Symbols;...Please refer to the documentation for more details.

223p chankora 16-06-2023 6 1   Download

(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

We obtain a differential equation with 2 boundary conditions for a relaxed elastic line in a Riemannian manifold. This differential equation, which is found with respect to constant sectional curvature G, geodesic curvature κ, and 2 boundary conditions, gives a more direct and more geometric approach to questions concerning a relaxed elastic line in a Riemannian manifold.

7p danhdanh27 07-01-2019 22 2   Download

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold.

17p danhdanh27 07-01-2019 22 1   Download

In this paper, the geometry of F-invariant submanifolds of a Kaehlerian product manifold is studied. The fundamental properties of these submanifolds are investigated such as pseudo umbilical, curvature invariant, totally geodesic, mixed geodesic submanifold and locally decomposable Riemannian product manifold.

15p danhdanh27 07-01-2019 15 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

Based on an extended space-time symmetry a new attempt to search for links between general relativity and quantum mechanics is proposed. A simplified cylindrical model of gravitational geometrical dynamics leads to a microscopic geodesic description of strongly curved extradimensional space-time which implies a duality between an emission law of microscopic gravitational waves and the quantum mechanical equations of free elementary particles. Consequently, the Heisenberg indeterminism would originate from the time-space curvatures.

9p thuyliebe 09-10-2018 30 0   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

Invariant measures for the geodesic flow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this flow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces.

37p noel_noel 17-01-2013 41 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. Notwithstanding the proof of ergodicity, and mixing, for geodesic flows on manifolds of negative curvature [15], [1], [35], ...

39p tuanloccuoi 04-01-2013 57 6   Download

We introduce a class of metric spaces which we call “bolic”. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov conjecture on higher signatures for any discrete group which admits a proper isometric action on a “bolic”, weakly geodesic metric space of bounded geometry. 1. Introduction This work has grown out of an attempt to give a purely KK-theoretic proof of a result of A. Connes and H. Moscovici ([CM], [CGM]) that hyperbolic groups satisfy the Novikov conjecture. ...

43p tuanloccuoi 04-01-2013 37 7   Download

Introduction to Differential Geometry and General Relativity Lecture Notes by Stefan Waner, with a Special Guest Lecture by Gregory C. Levine Department of Mathematics, Hofstra University These notes are dedicated to the memory of Hanno Rund. TABLE OF CONTENTS 1. Preliminaries: Distance, Open Sets, Parametric Surfaces and Smooth Functions 2. Smooth Manifolds and Scalar Fields 3. Tangent Vectors and the Tangent Space 4. Contravariant and Covariant Vector Fields 5. Tensor Fields 6. Riemannian Manifolds 7. Locally Minkowskian Manifolds: An Introduction to Relativity 8.

128p khangoc2391 11-08-2012 53 1   Download