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Stokes' Theorem on Smooth Manifolds
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

A proof of Stokes' theorem on smooth manifolds is given, complete with prerequisite results in tensor algebra and differential geometry. The essay assumes familiarity with multi-variable calculus and linear algebra, as well as a basic understanding of point-set topology. Stokes' theorem is then applied to the conservation of energy-momentum in general relativity under the existence of so called Killing vectors.

Abstract [sv]

Stokes sats för släta mångfalder bevisas, komplett med nödvändiga resultat från tensoralgebran och differentialgeometrin. Uppsatsen förutsätter förtrogenhet med flervariabelanalys och linjär algebra, samt en grundläggande förståelse för allmän topologi. Stokes sats appliceras sedan till bevarande av energi-momentum i allmän relativitetsteori under existensen av so kallade Killingvektorer.

Place, publisher, year, edition, pages
2016.
National Category
Geometry
Identifiers
URN: urn:nbn:se:umu:diva-125404OAI: oai:DiVA.org:umu-125404DiVA: diva2:967850
Educational program
Bachelor of Science in Physics and Applied Mathematics
Supervisors
Examiners
Available from: 2016-09-14 Created: 2016-09-09 Last updated: 2016-09-14Bibliographically approved

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fulltext(1206 kB)9 downloads
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Type fulltextMimetype application/pdf

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Jörgenfelt, Erik
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Department of Mathematics and Mathematical Statistics
Geometry

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