High Quality Content by WIKIPEDIA articles! 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. 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 x M is the flow domain. For each p ? M the map Dp ? M is the unique maximal integral curve of V starting at p. A global flow is one whose flow domain is all of R x 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.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.