Vektorska polja na sferah

delo diplomskega seminarja

Mark Baltič (Author), Aleš Vavpetič (Mentor)

Abstract

V diplomskem delu si ogledamo nekaj dejstev o obstoju neničelnega zveznega tangentnega vektorska polja na $n$-dimenzionalnih sferah. Najprej eksplicitno pokažemo konstrukcijo oz. nakažemo neobstoj takega vektorskega polja pri nižjih dimenzijah, nato pa idejo posplošimo na višje dimenzije. Pri dveh dimenzijah si ogledamo tudi druge objekte in nakažemo indikator, ki določi število izoliranih točk, kjer vektorsko polje izgine. Kot posledico glavnega izreka dokažemo tudi Browerjev izrek o negibni točki.

Keywords

matematika;tangentna vektorska polja;sfera;Browerjev izrek o negibni točki;Eulerjeva karakteristika;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Baltič]
UDC:	515.1
COBISS:	18394969
Views:	753
Downloads:	251
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Hairy ball theorem
Secondary abstract:	In this thesis we show some facts about existence of a non vanishing continuous tangent vector field on a $n$-dimensional sphere. At first we explicitly construct such vector field or we indicate the non existence of such vector field at low dimensions and then we generalize the idea to higher dimensions. In the two-dimensional case we also examine other objects and point out the indicator that sets the number of isolated points at which the vector field vanishes. As a consequence of our main theorem we also prove the Brower fixed-point theorem.
Secondary keywords:	mathematics;tangent vector fields;sphere;Brouwer fixed-point theorem;Euler characteristic;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	25 str.
ID:	10937952