Plohe konstantne srednje zakrivljenosti u Minkowskijevom prostoru

master's thesis

• Author: Davor Devald
• Mentor: Željka Milin-Šipuš (mentor)
• Committee member: Željka Milin-Šipuš (predsjednik povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Ozren Perše (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Plohe konstantne srednje zakrivljenosti (\(H = const.\)) sadrže dvije velike klase ploha - tzv. minimalne plohe (\(H=0\)) i tzv. cmc-plohe, odnosno prave plohe konstantne srednje zakrivljenosti (\(H = const. \neq 0\)). U euklidskoj geometriji, među njih spadaju, primjerice, helikoid i katenoid kao minimalne plohe te sfera i Delaunayeve plohe kao cmc-plohe. Cilj ovog diplomskog rada je analizirati analogne plohe u Minkowskijevom prostoru, tj. prostoru čija metrika nije pozitivno definitna, nego općenito nedegenerirana (pseudo-Riemannov prostor).

Abstract (english)

Surfaces of constant mean curvature (\(H = const.\)) contain two large classes of surfaces - minimal surfaces (\(H=0\)) and cmc-surfaces or surfaces of constant mean curvature (\(H = const. \neq 0\)). In euclidean geometry, they include, for example, helicoid and catenoid as minimal surfaces and the sphere and Delaunay surfaces as cmc-surfaces. The aim of this master’s thesis is to analyse analogue surfaces in the Minkowski space, a space whose metric isn’t positively definite, but is generally non-degenerate (a pseudo-Riemannian space).

• Keywords: plohe konstantne srednje zakrivljenosti; minimalne plohe; cmc-plohe; prave plohe konstantne srednje zakrivljenosti; Minkowskijev prostor; pseudo-Riemannov prostor
• Keywords (english): surfaces of constant mean curvature; minimal surfaces; cmc-surfaces; surfaces of constant mean curvature; Minkowski space; pseudo-Riemannian space
• Language: croatian
• URN:NBN: urn:nbn:hr:217:506214
• 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: 2018-01-25 11:14:23