Vector flow

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:

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.