Analytic geometry of homogeneous spaces
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StatusThe thesis was presented on the 5 July, 2017Approved by NCAA on the 11 May, 2018 Abstract – 0.17 Mb / in romanian – 0.17 Mb / in englishThesisCZU 514.742.2:514.120/514.140
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Keywords
Homogeneous space, Riemannian space, Klein geometry, projective metric, analytic geometrySummary
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.
Oficial Reviewers
- Macarov Vitalii
doctor habilitat în științe fizico-matematice, profesor universitar, Universitatea de Stat din Moscova, Rusia - Balan Vladimir
doctor în matematică, profesor universitar, Universitatea Politehnică din București, România
Council's Members
- Mitrofan Cioban, president
doctor habilitat, professor - Dumitru Cozma, secretary
doctor habilitat, associate professor (docent) - Ion Guţul , member
doctor, associate professor (docent), Institute of Mathematics and Computer Science - Sergiu Cataranciuc,
doctor habilitat, professor, Moldova State University - Moroianu Sergiu, membru
doctor în matematică, profesor universitar, Institutul de Matematică al Academiei Române, România
Theses
