E Book

Geometric Mechanics on Riemannian Manifolds



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.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 Schrödinger'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. Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter. 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.


Ketersediaan

9780817644215Koleksi E BookTersedia

Informasi Detil

Judul Seri
-
No. Panggil
-
Penerbit Birkhauser : Boston.,
Deskripsi Fisik
XVI, 278 p. 26 illus.online resource.
Bahasa
English
ISBN/ISSN
9780817644215
Klasifikasi
515.2433
Tipe Isi
-

Informasi Lainnya

Anak judul
Applications to Partial Differential Equations
Judul asli
-
DOI/URL
https://doi.org/10.1007/b138771

Versi lain/terkait

Tidak tersedia versi lain




Informasi


DETAIL CANTUMAN


Kembali ke sebelumnyaDetail XMLCite this