Primorac Gajčić, Ljiljana (2016) Mappings of ruled surfaces in Minkowski space. Doctoral thesis, Faculty of Science > Department of Mathematics.

PDF
Language: Croatian Download (2MB)  Preview 
Abstract
In this dissertation we study mappings of ruled surfaces in Minkowski space, special ambient space in which, with respect to defined pseudometrics, we distinguish three types of vectors, curves and surfaces. Ruled surfaces are surfaces that admit a parameterization of the form $f(u, v)=c(u) +ve(u)$, where $u, v$ are real numbers. The curve $c$ is called the base curve and the straight lines determined by direction vectors $e(u)$ are called the rulings of a ruled surface. In Preliminaries of the thesis we give an overview of basic concepts and theorems of Minkowski space, local theory of surfaces in Minkowski space, as well as their classification with respect to the causal character of the base curve, respectively rulings of ruled surface. In Chapter 2 we studied isometries of ruled surfaces, with particular interest in analyzing the conditions when given mapping preserves rulings of ruled surfaces, socalled Minding isometry. This mapping is studied for three relevant classes of ruled surfaces that appear in the Minkowski space. Special attention was given to surfaces that have no Euclidean counterparts, and we introduced the concept of nullruled surface of constant slope and gave theorems for their characterizations. In Chapters 3, respectively 4 we studied conformal, respectively areapreserving mappings for every class of ruled surfaces, also with additional condition that those mappings preserve rulings of ruled surface. In Chapter 5 we studied the invariants of Minding isometries of ruled surfaces in $n$dimensional Minkowski space, $\mathbb{R}_1^n$.
Item Type:  Thesis (Doctoral thesis) 

Keywords:  Minkowski space, ruled surfaces, local isometry, Minding isometry, conformal mapping, areapreserving mapping, (k + 1)ruled surfaces 
Supervisor:  MilinŠipuš, Željka 
Date:  2016 
Number of Pages:  93 
Subjects:  NATURAL SCIENCES > Mathematics NATURAL SCIENCES > Mathematics > Geometry and Topology 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  08 Nov 2016 11:35 
Last Modified:  08 Nov 2016 11:35 
URI:  http://digre.pmf.unizg.hr/id/eprint/5265 
Actions (login required)
View Item 