Geometric structures invariant to symmetries

B 2012

Geometric structures invariant to symmetries

GREGOROVIČ, Jan

Basic information

Original name

Geometric structures invariant to symmetries

Authors

GREGOROVIČ, Jan (203 Czech Republic, guarantor, belonging to the institution)

Edition

1. vyd. Brno, 91 pp. FOLIA Mathematica 18, 2012

Publisher

Masaryk University

Other information

Language

English

Type of outcome

Book on a specialized topic

Field of Study

10101 Pure mathematics

Country of publisher

Czech Republic

Confidentiality degree

is not subject to a state or trade secret

Publication form

printed version "print"

References:

Munishop

RIV identification code

RIV/00216224:14310/12:00058001

Organization unit

Faculty of Science

ISBN

978-80-210-6010-4

DOI

10.5817/CZ.MUNI.M210-6010-2012

Keywords in English

symmetric spaces; geometric structures; Cartan geometries; parabolic geometries; homogeneous spaces; extension functors

Abstract

In the original language

The aim of this book is to generalize symmetric spaces to several geometric strctures. The first and third chapter of this work contain description of several geometric structures, for which we want to define the symmetries. This is done in the second chapter and at the end end of the third chapter. The second chapter also explains, how the classical symmetric spaces fit in our approach, and investigates geometric structures on symmetric spaces. In the fourth and fifth chapters, we investigate and construct examples of symmetric parabolic geometries in the simplest cases. In fact, we obtain classification of non-flat symmetric AHS-structures and parabolic contact structures in the case when the groups generated by the symmetries are semisimple, and we explicitly construct many of them. For the convenience of the reader, the appendices display tables containing the classification of simple symmetric spaces and tables containing the gradings associated to the parabolic geometries, which we are investigating.

Links

GD201/09/H012, research and development project

Name: Algebraické a geometrické metody a struktury

Investor: Czech Science Foundation, Algebraic and geometric methods and structures

Cite

GREGOROVIČ, Jan. Geometric structures invariant to symmetries. 1. vyd. Brno: Masaryk University, 2012, 91 pp. FOLIA Mathematica 18. ISBN 978-80-210-6010-4. Available from: https://dx.doi.org/10.5817/CZ.MUNI.M210-6010-2012.

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   author = {Gregorovič, Jan},
   address = {Brno},
   doi_mu = {http://dx.doi.org/10.5817/CZ.MUNI.M210-6010-2012},
   edition = {1. vyd.},
   keywords = {symmetric spaces; geometric structures; Cartan geometries; parabolic geometries; homogeneous spaces; extension functors},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Brno},
   isbn = {978-80-210-6010-4},
   publisher = {Masaryk University},
   title = {Geometric structures invariant to symmetries},
   url = {https://munishop.muni.cz/obchod/knihy/geometric-structures-invariant-to-symmetries-00003026010},
   year = {2012}
}

TY  - BOOK
ID  - 1080551
AU  - Gregorovič, Jan
PY  - 2012
TI  - Geometric structures invariant to symmetries
VL  - FOLIA Mathematica 18
PB  - Masaryk University
CY  - Brno
SN  - 9788021060104
KW  - symmetric spaces
KW  - geometric structures
KW  - Cartan geometries
KW  - parabolic geometries
KW  - homogeneous spaces
KW  - extension functors
UR  - https://munishop.muni.cz/obchod/knihy/geometric-structures-invariant-to-symmetries-00003026010
N2  - The aim of this book is to generalize symmetric spaces to several geometric strctures. The first and third chapter of this work contain description of several geometric structures, for which we want to define the symmetries. This is done in the second chapter and at the end end of the third chapter. The second chapter also explains, how the classical symmetric spaces fit in our approach, and investigates geometric structures on symmetric spaces. In the fourth and fifth chapters, we investigate and construct examples of symmetric parabolic geometries in the simplest cases. In fact, we obtain classification of non-flat symmetric AHS-structures and parabolic contact structures in the case when the groups generated by the symmetries are semisimple, and we explicitly construct many of them. For the convenience of the reader, the appendices display tables containing the classification of simple symmetric spaces and tables containing the gradings associated to the parabolic geometries, which we are investigating.
ER  -

GREGOROVIČ, Jan. \textit{Geometric structures invariant to symmetries}. 1. vyd. Brno: Masaryk University, 2012, 91 pp. FOLIA Mathematica 18. ISBN~978-80-210-6010-4. Available from: https://dx.doi.org/10.5817/CZ.MUNI.M210-6010-2012.

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