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Bäcklund transformations for minimal surfaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

In this thesis, we study a Bäcklund transformation for minimal surfaces - surfaces with vanishing mean curvature - transforming a given minimal surface into a possible infinity of new ones.

The transformation, also carrying with it mappings between solutions to the elliptic Liouville equation, is first derived by using geometrical concepts, and then by using algebraic methods alone - the latter we have not been able to find elsewhere. We end by exploiting the transformation in an example, transforming the catenoid into a family of new minimal surfaces.

Place, publisher, year, edition, pages
2015. , 53 p.
Keyword [en]
Bäcklund transformations, Liouville equation, minimal surfaces, Ribaucour transformations, Thybaut transformations.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-119914ISRN: LiTH-MAT-EX--2015/04--SEOAI: oai:DiVA.org:liu-119914DiVA: diva2:833320
Subject / course
Applied Mathematics
Supervisors
Examiners
Available from: 2015-06-30 Created: 2015-06-30 Last updated: 2015-09-21Bibliographically approved

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Bäcklund transformations for minimal surfaces(735 kB)199 downloads
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
  • html
  • text
  • asciidoc
  • rtf