Title Geometric mechanics on Riemannian manifolds : applications to partial differential equations / Ovidiu Calin, Der-Chen Chang

Published Boston : Birkhäuser, ©2005

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Description 1 online resource (xv, 278 pages) Series Applied and Numerical Harmonic Analysis Applied and numerical harmonic analysis. Contents Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators -- Mechanical Curves Summary "Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrodinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler-Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible." "Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas."--Jacket Bibliography Includes bibliographical references (pages 271-273) and index In Springer eBooks Subject Riemannian manifolds. Global Riemannian geometry. Mechanics, Analytic. Differential equations, Partial. Mathematics. Fourier Analysis Mathematics Variedades riemannianas Mecánica analítica Differential equations, Partial Global Riemannian geometry Mechanics, Analytic Riemannian manifolds Riemannsche Geometrie -- Theoretische Mechanik -- Partielle Differentialgleichung. Theoretische Mechanik -- Riemannsche Geometrie -- Partielle Differentialgleichung. Partielle Differentialgleichung -- Theoretische Mechanik -- Riemannsche Geometrie. Form Electronic book Author Calin, Ovidiu Chang, Der-chen E LC no. 2004046386 ISBN 0817643540 9780817643546 9780817644215 0817644210 1281335754 9781281335753

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