"Differential Geometry: Curvature and Holonomy" by Austin Christian

Abstract

We develop the basic language of differential geometry, including smooth manifolds, bundles, and differential forms. Once this background is established, we explore parallelism in smooth manifolds -- in particular, in Riemannian manifolds -- and conclude by presenting a proof of the Ambrose-Singer theorem, which relates parallelism (holonomy) to curvature in principal bundles.

Date of publication

Spring 5-5-2015

Document Type

Thesis

Language

english

Persistent identifier

http://hdl.handle.net/10950/266

Included in

Mathematics Commons

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