Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Grundläggande hyperbolisk geometri
Karlstad University, Faculty of Technology and Science.
2006 (Swedish)Independent thesis Advanced level (degree of Magister), 20 points / 30 hpStudent thesisAlternative title
Elements of Hyperbolic Geometry (English)
Abstract [sv]

I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet.

Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar.

Abstract [en]

In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880.

The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles.

Place, publisher, year, edition, pages
2006. , p. 75
Keywords [en]
Hyperbolic Geometry, Möbius transformation, Gauss-Bonnét, Geodetic line, isometry, rotation, translation, cross-ratio, hyperbolic arclength
Keywords [sv]
Hyperbolisk geometri, Möbiusavbildningar, Gauss-Bonnét, geodetisk linje, isometri, rotation, translation, anharmoniskt förhållande, hyperbolisk båglängd
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-211OAI: oai:DiVA.org:kau-211DiVA, id: diva2:5853
Presentation
2006-05-23
Uppsok
fysik/kemi/matematik
Supervisors
Examiners
Available from: 2006-06-21 Created: 2006-06-21

Open Access in DiVA

fulltext(568 kB)554 downloads
File information
File name FULLTEXT01.pdfFile size 568 kBChecksum MD5
df9097d93b15d2f23e4480bdbdda7417b3e4c7c8ba8219d86690f1b67a235cae0568de2a
Type fulltextMimetype application/pdf

By organisation
Faculty of Technology and Science
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 554 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 732 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf