Related Books

Vector Fields on Manifolds
Language: en
Pages: 23
Authors: Michael Francis Atiyah
Categories: Mathematics
Type: BOOK - Published: 1970 - Publisher: Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic
Vector Fields on Manifolds
Language: en
Pages: 30
Authors: Michael Francis Atiyah
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer

This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic
Harmonic Vector Fields
Language: en
Pages: 529
Authors: Sorin Dragomir, Domenico Perrone
Categories: Computers
Type: BOOK - Published: 2011-10-26 - Publisher: Elsevier

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion
Vector Fields on Singular Varieties
Language: en
Pages: 242
Authors: Jean-Paul Brasselet, José Seade, Tatsuo Suwa
Categories: Mathematics
Type: BOOK - Published: 2009-12-17 - Publisher: Springer Science & Business Media

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field,
Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
Language: en
Pages: 539
Authors: Taeyoung Lee, Melvin Leok, N. Harris McClamroch
Categories: Mathematics
Type: BOOK - Published: 2017-08-14 - Publisher: Springer

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce