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CNAA / Theses / 2017 / July /

Analytic geometry of homogeneous spaces


Author: Popa Alexandru
Degree:doctor of
Speciality: 01.01.04 - Geometry and topology
Year:2018
Scientific adviser: Florin Damian
doctor, associate professor (docent)
Institution: Institute of Mathematics and Computer Science of the ASM

Status

The thesis was presented on the 5 July, 2017
Approved by NCAA on the 11 May, 2018

Abstract

Adobe PDF document0.17 Mb / in romanian
Adobe PDF document0.17 Mb / in english

Thesis

CZU 514.742.2:514.120/514.140

Adobe PDF document 1.60 Mb / in english
187 pages


Keywords

Homogeneous space, Riemannian space, Klein geometry, projective metric, analytic geometry

Summary

The thesis is written in English and consists of: introduction, three chapters, general conclusions and recommandations, appendix, 210 bibliography titles, 140 pages of main text, 27 figures, 9 algorithms, 5 tables. The obtained results were published in 9 scientific papers.

Domain of research: Geometry of homogeneous spaces.

Goals and objectives: The goal of the research is to provide a toolchain that can be used to study of homogeneous spaces by means of linear algebra. The objectives of the research are: introduction of the new concept of the space signature, construction of homogeneous space based on signature concept, construction of the model of homogeneous space with given signature, expression of the measurement of different geometric quantities via signature, different applications of the analytic geometry of homogeneous spaces.

Scientific innovation of obtained results:
• Analytic geometry is developed in linear algebra language, even for non–linear spaces.
• One universal theory is developed that uses the elements of space signature as parameters.

Important scientific problem solved: The investigation of the homogeneous spaces with linear methods via concept of the signature.
Theoretical and practical value of the work: Rezultatele prezentate în teză sunt noi, au un caracter teoretic și cu ajutorul conceptului de signatură prezintă o teorie generală a spațiilor omogene.
Implementation of scientific rezults:
• New results can be used in investigation of the problems of differential geometry, in theoretic physics and in other domains where notion of the signature can be applied in the given sense.
• The thesis can be used as the didactic support for optional courses in the university and doctoral studies.