Gauge theory and calibrated geometry. I. (English) Zbl 0957.58013

The author studies a new natural interaction between Yang-Mills connections, which are critical points of a Yang-Mills action associated to a vector bundle, and minimal submanifolds, which have been studied a lot for several years in classical differential geometry and the calculus of variations.
All the results of this paper can be generalized to the case of the Yang-Mills-Higgs equation as it is mentioned in the paper.
In the last chapter of this paper the author discusses compactification of the moduli space of anti-self-dual instantons and some related problems.


58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI arXiv EuDML Link