Notes on symmetric conformal geometries

Jan Gregorovič; Lenka Zalabová

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 5, page 287-296
  • ISSN: 0044-8753

Abstract

top
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or covered by a pseudo-Riemannian symmetric space, where the covering is a conformal map. We construct examples of locally flat symmetric conformal geometries that are not pseudo-Riemannian symmetric spaces.

How to cite

top

Gregorovič, Jan, and Zalabová, Lenka. "Notes on symmetric conformal geometries." Archivum Mathematicum 051.5 (2015): 287-296. <http://eudml.org/doc/276200>.

@article{Gregorovič2015,
abstract = {In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or covered by a pseudo-Riemannian symmetric space, where the covering is a conformal map. We construct examples of locally flat symmetric conformal geometries that are not pseudo-Riemannian symmetric spaces.},
author = {Gregorovič, Jan, Zalabová, Lenka},
journal = {Archivum Mathematicum},
keywords = {conformal geometry; symmetric space; parallel Weyl tensor},
language = {eng},
number = {5},
pages = {287-296},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Notes on symmetric conformal geometries},
url = {http://eudml.org/doc/276200},
volume = {051},
year = {2015},
}

TY - JOUR
AU - Gregorovič, Jan
AU - Zalabová, Lenka
TI - Notes on symmetric conformal geometries
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 5
SP - 287
EP - 296
AB - In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or covered by a pseudo-Riemannian symmetric space, where the covering is a conformal map. We construct examples of locally flat symmetric conformal geometries that are not pseudo-Riemannian symmetric spaces.
LA - eng
KW - conformal geometry; symmetric space; parallel Weyl tensor
UR - http://eudml.org/doc/276200
ER -

References

top
  1. Čap, A., Melnick, K., Essential Killing fields of parabolic geometries: projective and conformal structures, Central European Journal of Mathematics 11 (12) (2013), 2053–2061. (2013) Zbl1286.53017MR3111705
  2. Čap, A., Slovák, J., 10.1090/surv/154/03, Math. Surveys and Monogr., vol. 154, Amer. Math. Soc., 2009. (2009) MR2532439DOI10.1090/surv/154/03
  3. Derdzinski, A., Roter, W., 10.2748/tmj/1199649875, Tohoku Math. J. 59 (4) (2007), 565–602. (2007) Zbl1146.53014MR2404206DOI10.2748/tmj/1199649875
  4. Gregorovič, J., Classification of invariant AHS-structures on semisimple locally symmetric spaces, Central European Journal of Mathematics 11 (12) (2013), 2062–2075. (2013) Zbl1300.53054MR3111706
  5. Gregorovič, J., Zalabová, L., On automorphisms with natural tangent action on homogeneous parabolic geometries, J. Lie Theory 25 (2015), 677–715. (2015) MR3384992
  6. Kruglikov, B., The, D., The gap phenomenon in parabolic geometries, arXiv:1303.1307. 
  7. Zalabová, L., 10.1016/j.difgeo.2009.03.001, Differential Geom. Appl. 27 (5) (2009), 605–622. (2009) Zbl1187.53036MR2567839DOI10.1016/j.difgeo.2009.03.001
  8. Zalabová, L., 10.1007/s10455-009-9177-5, Ann. Global Anal. Geom. 37 (2) (2010), 125–141. (2010) Zbl1188.53026MR2578261DOI10.1007/s10455-009-9177-5
  9. Zalabová, L., A non–homogeneous, symmetric contact projective structure, Central European Journal of Mathematics 12 (6) (2014), 879–886. (2014) Zbl1302.53058MR3179989

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.