In mathematical physics, the wave maps equation is a geometric

wave equation The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light ...

that solves :

D^\alpha \partial_\alpha u = 0

where

D

is a connection. It can be considered a natural extension of the

for

Riemannian manifolds In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined. Euclidean space, the n-sphere, hyperbolic space, and smooth surfaces in ...

References

Equations {{applied-math-stub