%0 Journal Article
%T The Yang-Mills functional and Laplace's equation on quantum Heisenberg manifolds
%A Sooran Kang
%J Mathematics
%D 2009
%I arXiv
%X In this paper, we discuss the Yang-Mills functional and a certain family of its critical points on quantum Heisenberg manifolds using noncommutative geometrical methods developed by A. Connes and M. Rieffel. In our main result, we construct a certain family of connections on a projective module over a quantum Heisenberg manifold that give rise to critical points of the Yang-Mills functional. Moreover, we show that this set of solutions can be described as a set of solutions to Laplace's equation on quantum Heisenberg manifolds.
%U http://arxiv.org/abs/0904.4291v1