Remarks on symmetries of parabolic geometries

Lenka Zalabová

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 357-368
  • ISSN: 0044-8753

Abstract

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We consider symmetries on filtered manifolds and we study the | 1 | -graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.

How to cite

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Zalabová, Lenka. "Remarks on symmetries of parabolic geometries." Archivum Mathematicum 042.5 (2006): 357-368. <http://eudml.org/doc/249833>.

@article{Zalabová2006,
abstract = {We consider symmetries on filtered manifolds and we study the $|1|$-graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.},
author = {Zalabová, Lenka},
journal = {Archivum Mathematicum},
keywords = {Cartan geometry; generalized structure; graded simple Lie algebra; homogeneous model; curvature},
language = {eng},
number = {5},
pages = {357-368},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Remarks on symmetries of parabolic geometries},
url = {http://eudml.org/doc/249833},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Zalabová, Lenka
TI - Remarks on symmetries of parabolic geometries
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 357
EP - 368
AB - We consider symmetries on filtered manifolds and we study the $|1|$-graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved geometries.
LA - eng
KW - Cartan geometry; generalized structure; graded simple Lie algebra; homogeneous model; curvature
UR - http://eudml.org/doc/249833
ER -

References

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  3. Čap A., Two constructions with parabolic geometries, Proceedings of the 25th Winter School on Geometry and Physics, Srní 2005 Rend. Circ. Mat. Palermo (2) Suppl. 79 (2006), 11–38 Zbl1120.53013MR2287124
  4. Kaup W., Zaitsev D., On symmetric Cauchy-Riemann manifolds, Adv. Math. 149 (2000), 145–181. Zbl0954.32016MR1742704
  5. Kobayashi S., Nomizu K., Foundations of Differential Geometry, Vol II, John Wiley & Sons, New York–London–Sydney, 1969. (1969) Zbl0175.48504MR0238225
  6. Sharpe R. W., Differential geometry: Cartan’s generalization of Klein’s Erlangen program, Graduate Texts in Mathematics 166, Springer-Verlag 1997. (1997) Zbl0876.53001MR1453120
  7. Slovák J., Parabolic geometries, Research Lecture Notes, Part of DrSc-dissertation, Masaryk University, 1997, IGA Preprint 97/11 (University of Adelaide). (1997) 
  8. Yamaguchi K., Differential systems associated with simple graded Lie algebras, Adv. Stud. Pure Math. 22 (1993), 413–494. (1993) Zbl0812.17018MR1274961

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