The three dimensional Fueter equation and divergence free frames

Details The three dimensional Fueter equation and divergence free frames The three dimensional Fueter equation and divergence free frames

2012-02-19

arxiv.org/abs/1202.4165v4

Mathematics

Symplectic Geometry

Section 5 on the gauged Fueter equation was added on 29 February 2012. Appendix B on the h-principle for divergence free frame

Scientific paper

A divergence free frame on a closed three manifold is called regular if every solution of the linear Fueter equation is constant and is called singular otherwise. The set of singular divergence free frames is an analogue of the Maslov cycle. Regular divergence free frames satisfy an analogue of the Arnold conjecture for flat hyperkaehler target manifolds. The Seiberg-Witten equations can be viewed as gauged versions of the Fueter equation, and so can the Donaldson-Thomas equations on certain seven dimensional product manifolds.

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