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Ricciflödet
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Ricci Flow (English)
Abstract [sv]

I den här uppsatsen studeras Ricciflödet på 3-dimensionella unimodulära Liegrupper med vänsterinvariant metrik. Satser gällande konvergens och långtidsbeteende hos metriken formuleras och bevisas. Ett nämnvärt resultat gällande det normaliserade Ricciflödet är konvergensen av en godtycklig vänsterinvariant metrik på SU(2) till en metrik med konstant krökning. Utöver detta formuleras och bevisas maximumprinciper på mångfalder. Några tillämpningar av dessa maximumprinciper på Ricciflödet som ger kontroll över krökningsstorheterna ges också.

Abstract [en]

In this paper, the Ricci flow on 3-dimensional unimodular Lie groups with left-invariant metric is studied. Theorems concerning convergence and long-time behavior of the metric under the Ricci flow are formulated and proved. A notable result concerning the normalized Ricci flow is the convergence of any left-invariant metric on SU(2) to a metric of constant curvature. Additionally, maximum principles on manifolds are formulated and proved. Some applications of these maximum principles to the Ricci flow which yield control over the curvature quantities are also given.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:113
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254702OAI: oai:DiVA.org:kth-254702DiVA, id: diva2:1334778
Supervisors
Examiners
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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Output format
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