Riemannov tenzor zakrivljenosti

master's thesis

• Author: Branimir Stojanović
• Mentor: Dragutin Svrtan (mentor)
• Mentor: Željka Milin-Šipuš (mentor)
• Committee member: Željka Milin-Šipuš (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Vjekoslav Kovač (član povjerenstva)
• Committee member: Ante Mimica (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prvo navodimo neka svojstva regularnih ploha u \(\mathbb{R}^3\), kao što je pojam Riemannovog tenzora definiran na tim plohama, i navodimo dokaz Gaussovog Veličanstvenog teorema. Nakon toga navodimo osnove diferencijalnih mnogostrukosti uključujući i pojam Riemannove metrike. Zatim obradujemo pojam Riemannovih mnogostrukosti i proučavamo neka njihova svojstva.

Abstract (english)

In this thesis we first recall some properties of the regular surfaces in \(\mathbb{R}^3\), like the notion of the Riemann tensor of this surfaces and present a proof of the Gauss’s Theorema Egregium. Afterwards we present basics of Differential manifolds including a concept of the Riemannian metric on. Then we elaborate the notion of a Riemannian manifolds and study some of its properties.

• Keywords: Riemannovog tenzor; regularne plohe; Gaussov Veličanstveni teorem; Riemannove metrika; Riemannove mnogostrukosti
• Keywords (english): Riemann tensor; regular surfaces; Gauss’s Theorema Egregium; Riemannian metric; Riemannian manifolds
• Language: croatian
• URN:NBN: urn:nbn:hr:217:342021
• 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: 2019-02-07 13:23:07