%0 Journal Article
%T Transparent connections over negatively curved surfaces
%A Gabriel P. Paternain
%J Mathematics
%D 2008
%I arXiv
%X Let $(M,g)$ be a closed oriented negatively curved surface. A unitary connection on a Hermitian vector bundle over $M$ is said to be transparent if its parallel transport along the closed geodesics of $g$ is the identity. We study the space of such connections modulo gauge and we prove a classification result in terms of the solutions of certain PDE that arises naturally in the problem. We also show a local uniqueness result for the trivial connection and that there is a transparent SU(2)-connection associated to each meromorphic function on $M$.
%U http://arxiv.org/abs/0809.4360v4