Vector Field

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Related to Tangent bundle section: Whitney sum, Vector bundle, Tangent vector bundle, Zero section

vector field

[′vek·tər ‚fēld]
The field of vectors arising from considering a system of differential equations on a differentiable manifold.
A function whose range is in a vector space.
A field which is characterized by a vector function.

Vector Field


a region, at each point P of which a vector a(P) is assigned. Mathematically, a vector field can be defined in a given region G by the vector function a(P) of the variable point P of this region. A whole series of physical phenomena and processes (for example, the vectors of the velocities of a moving fluid’s particles at each moment of time form a vector field) lead to the concept of a vector field. Vector-field theory has been extensively developed and has diverse applications in various branches of natural science.


Budak, B. M., and S. V. Fomin. Kratnye integraly i riady, 2nd ed.Moscow, 1967.