# Wave maps equation

In mathematical physics, the wave maps equation is a geometric wave equation that solves

${\displaystyle D^{\alpha }\partial _{\alpha }u=0}$

where ${\displaystyle D}$ is a connection.[1][2]

It can be considered a natural extension of the wave equation for Riemannian manifolds.[3]

## References

1. ^ Tataru, Daniel (1 January 2005). "Rough solutions for the wave maps equation". American Journal of Mathematics. 127 (2): 293–377. doi:10.1353/ajm.2005.0014.
2. ^ Tataru, Daniel (2004). "The wave maps equation" (PDF). Bulletin of the American Mathematical Society (N.S.). 41 (2): 185–204. Zbl 1065.35199.
3. ^ http://www.math.ucla.edu/~tao/preprints/wavemaps.pdf