
TL;DR
This paper classifies cohomologically trivial SO(3)-pairs with finite Fourier series on Riemannian surfaces, providing a full classification of transparent pairs in negatively curved cases using Bäcklund transformations.
Contribution
It introduces a classification of transparent pairs on Riemannian surfaces, especially in negatively curved cases, via Bäcklund transformations, advancing understanding of such geometric structures.
Findings
Complete classification of SO(3)-transparent pairs on negatively curved surfaces.
Use of Bäcklund transformations to characterize cohomologically trivial pairs.
Identification of conditions for finite Fourier series in the classification.
Abstract
Let be a closed orientable Riemannian surface. Consider an SO(3)-connection and a Higgs field . The pair naturally induces a cocycle over the geodesic flow of . We classify (up to gauge transformations) cohomologically trivial pairs with finite Fourier series in terms of a suitable B\"acklund transformation. In particular, if is negatively curved we obtain a full classification of SO(3)-transparent pairs.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Geometric Analysis and Curvature Flows
