Transparent connections over negatively curved surfaces

Details Transparent connections over negatively curved surfaces Transparent connections over negatively curved surfaces

2008-09-25

arxiv.org/abs/0809.4360v4

Mathematics

Differential Geometry

Minor correction to the proof of Lemma 6.5

Scientific paper

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 $M$.

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