wave maps equation
In mathematical physics, the wave maps equation is a geometric wave equation that solves
:
where is a connection.{{cite journal|last=Tataru|first=Daniel|title=Rough solutions for the wave maps equation|journal=American Journal of Mathematics|date=1 January 2005|volume=127|issue=2|pages=293–377|doi=10.1353/ajm.2005.0014|citeseerx=10.1.1.631.6746|s2cid=53521030}}{{cite journal | zbl=1065.35199 | last=Tataru | first=Daniel | title=The wave maps equation | journal=Bulletin of the American Mathematical Society |series=New Series | volume=41 |number=2 | pages=185–204 | year=2004 | url=http://www.ams.org/journals/bull/2004-41-02/S0273-0979-04-01005-5/S0273-0979-04-01005-5.pdf | doi=10.1090/S0273-0979-04-01005-5 | doi-access=free }}
It can be considered a natural extension of the wave equation for Riemannian manifolds.{{Cite web |last=Tao |first=Terence |title=Wave Maps (preprint) |url=https://www.math.ucla.edu/~tao/preprints/wavemaps.pdf |access-date=2023-10-04 |website=Department of Mathematics, UCLA}}