Thurstonove geometrije

master's thesis

• Author: Kristijan Kilassa Kvaternik
• Mentor: Željka Milin-Šipuš (mentor)
• Committee member: Željka Milin-Šipuš (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Na početku ovog rada definiramo osnovne pojmove potrebne za razumijevanje Thurstonovih geometrija: pojmove Riemannove mnogostrukosti i geometrijske strukture. Nakon toga dajemo kratki pregled geometrijskih struktura u 2 i 3 dimenzije te opisujemo svih 8 Thurstonovih geometrija. U dvjema od tih geometrija, Sol i Nil, određujemo neke klase krivulja i ploha (geodetske i translacijske krivulje te minimalne translacijske plohe).

Abstract (english)

At the beginning of this thesis we define basic notions necessary for understanding Thurston geometries: the notion of Riemannian manifold and geometric structure. After that we give a short review of all geometric structures in 2 and 3 dimensions and describe all of 8 Thurston geometries. In two of them, Sol and Nil, we determine some classes of curves and surfaces (geodesics, translation curves and minimal translation surfaces).

• Keywords: Thurstonove geometrije; Riemannove mnogostrukosti; geometrijske strukture; Sol; Nil; geodetske krivulje; translacijske krivulje; minimalne translacijske plohe
• Keywords (english): Thurston geometries; Riemannian maniforld; geometric structure; Sol; Nil; geodesics; translation curves; minimal translation surfaces
• Language: croatian
• URN:NBN: urn:nbn:hr:217:755484
• Study programme: Title: Pure Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-08 12:11:46