Transparent connections over negatively curved surfaces

DOI10.3934/jmd.2009.3.311zbMath1185.53024arXiv0809.4360OpenAlexW2962850065MaRDI QIDQ2268270

Gabriel P. Paternain

Publication date: 10 March 2010

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.4360

zbMATH Keywords

geodesic flowcomplex Hermitian vector bundlethe Livšic theorem for non-abelian cocyclestransparent connection

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Second-order elliptic equations (35J15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Geodesics in global differential geometry (53C22) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (8)

The X-ray transform for connections in negative curvature ⋮ Tensor tomography on surfaces ⋮ Transparent pairs ⋮ The attenuated ray transform for connections and Higgs fields ⋮ Carleman estimates for geodesic X-ray transforms ⋮ Tensor tomography: progress and challenges ⋮ Bäcklund transformations for transparent connections ⋮ On the range of the attenuated magnetic ray transform for connections and Higgs fields

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