|
In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different contexts, including differential topology, Riemannian geometry and Lie group theory. These related concepts are explored in a spectrum of articles: *exponential map (Riemannian geometry) * *matrix exponential * *exponential function *infinitesimal generator (→ Lie group) *integral curve (→ vector field) *one-parameter subgroup *flow (geometry) * *geodesic flow * *Hamiltonian flow * *Ricci flow * *Anosov flow *injectivity radius (→ glossary) ==Vector flow in differential topology== Relevant concepts: ''(flow, infinitesimal generator, integral curve, complete vector field)'' Let ''V'' be a smooth vector field on a smooth manifold ''M''. There is a unique maximal flow ''D'' → ''M'' whose infinitesimal generator is ''V''. Here ''D'' ⊆ R × ''M'' is the flow domain. For each ''p'' ∈ ''M'' the map ''D''''p'' → ''M'' is the unique maximal integral curve of ''V'' starting at ''p''. A global flow is one whose flow domain is all of R × ''M''. Global flows define smooth actions of R on ''M''. A vector field is complete if it generates a global flow. Every vector field on a compact manifold without boundary is complete. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vector flow」の詳細全文を読む スポンサード リンク
|