Mappings of ruled surfaces in Minkowski space

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

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Abstract

In this dissertation we study mappings of ruled surfaces in Minkowski space, special ambient space in which, with respect to defined pseudo-metrics, 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, so-called 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 null-ruled surface of constant slope and gave theorems for their characterizations. In Chapters 3, respectively 4 we studied conformal, respectively area-preserving 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: Milin-Šipuš, 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

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