Vector Field

A Map ${\bf f}: \Bbb{R}^n \mapsto \Bbb{R}^n$ which assigns each ${\bf x}$ a Vector Function ${\bf f}({\bf x})$. Flows are generated by vector fields and vice versa. A vector field is a Section of its Tangent Bundle.

See also Flow, Scalar Field, Seifert Conjecture, Tangent Bundle, Vector, Wilson Plug

References

Gray, A. ``Vector Fields $\Bbb{R}^n$'' and ``Derivatives of Vector Fields $\Bbb{R}^n$.'' §9.4-9.5 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 171-174 and 175-178, 1993.

Morse, P. M. and Feshbach, H. ``Vector Fields.'' §1.2 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 8-21, 1953.