Notes on symmetric conformal geometries

Jan Gregorovič; Lenka Zalabová

Archivum Mathematicum (2015)

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

Abstract

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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

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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

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  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
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  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

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