Remarks on Special Symplectic Connections

Martin Panák; Vojtěch Žádník

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 5, page 491-510
  • ISSN: 0044-8753

Abstract

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The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over the homogeneous model of the corresponding parabolic contact structure.

How to cite

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Panák, Martin, and Žádník, Vojtěch. "Remarks on Special Symplectic Connections." Archivum Mathematicum 044.5 (2008): 491-510. <http://eudml.org/doc/250503>.

@article{Panák2008,
abstract = {The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over the homogeneous model of the corresponding parabolic contact structure.},
author = {Panák, Martin, Žádník, Vojtěch},
journal = {Archivum Mathematicum},
keywords = {special symplectic connections; parabolic contact geometries; Weyl structures and connections; special symplectic connection; parabolic contact geometry; Weyl structure; Weyl connection},
language = {eng},
number = {5},
pages = {491-510},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Remarks on Special Symplectic Connections},
url = {http://eudml.org/doc/250503},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Panák, Martin
AU - Žádník, Vojtěch
TI - Remarks on Special Symplectic Connections
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 5
SP - 491
EP - 510
AB - The notion of special symplectic connections is closely related to parabolic contact geometries due to the work of M. Cahen and L. Schwachhöfer. We remind their characterization and reinterpret the result in terms of generalized Weyl connections. The aim of this paper is to provide an alternative and more explicit construction of special symplectic connections of three types from the list. This is done by pulling back an ambient linear connection from the total space of a natural scale bundle over the homogeneous model of the corresponding parabolic contact structure.
LA - eng
KW - special symplectic connections; parabolic contact geometries; Weyl structures and connections; special symplectic connection; parabolic contact geometry; Weyl structure; Weyl connection
UR - http://eudml.org/doc/250503
ER -

References

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  1. Bryant, R., 10.1090/S0894-0347-01-00366-6, J. Amer. Math. Soc. 14 (2) (2001), 623–715. (2001) Zbl1006.53019MR1824987DOI10.1090/S0894-0347-01-00366-6
  2. Cahen, M., Gutt, S., Schwachhöfer, L., Construction of Ricci–type connections by reduction and induction, The breadth of symplectic and Poisson geometry, 2005, pp. 41–57. (2005) Zbl1079.53117MR2103002
  3. Cahen, M., Schwachhöfer, L., Special symplectic connections, eprint arXiv:math/0402221v2. MR2232865
  4. Čap, A., 10.1515/crll.2005.2005.582.143, J. Reine Angew. Math. 582 (2005), 143–172. (2005) Zbl1075.53022MR2139714DOI10.1515/crll.2005.2005.582.143
  5. Čap, A., Gover, A. R., 10.1090/S0002-9947-01-02909-9, Trans. Amer. Math. Soc. 354 (2002), 1511–1548. (2002) Zbl0997.53016MR1873017DOI10.1090/S0002-9947-01-02909-9
  6. Čap, A., Slovák, J., Parabolic Geometries, to appear in Math. Surveys Monogr., 2008. 
  7. Čap, A., Slovák, J., Weyl Structures for Parabolic Geometries, Math. Scand. 93 (2003), 53–90. (2003) Zbl1076.53029MR1997873
  8. Chu, B. Y., 10.1090/S0002-9947-1974-0342642-7, Trans. Amer. Math. Soc. 197 (1974), 145–159. (1974) MR0342642DOI10.1090/S0002-9947-1974-0342642-7
  9. Fox, D. J., Contact projective structures, Indiana Univ. Math. J. 54 (6) (2005), 1547–1598. (2005) Zbl1093.53083MR2189678
  10. Jacobowitz, H., An introduction to CR structures, Math. Surveys Monogr. 32 (1990). (1990) Zbl0712.32001
  11. Panák, M., Schwachhöfer, L., Bochner–Kaehler metrics and connections of Ricci–type, Proceedings of the 10th Conference on Differential Geometry and its Applications, Olomouc 2007, World Scientific, 2008, pp. 339–352. (2008) Zbl1162.53324MR2462805
  12. Pikulin, S. V., Tevelev, E. A., 10.1007/BF01597137, Transform. Groups 6 (2) (2001), 193–198. (2001) Zbl1009.22014MR1835673DOI10.1007/BF01597137
  13. Slovák, J., Parabolic geometries, Tech. report, IGA preprint 97/11, Univ. of Adelaide, 1997. (1997) 
  14. Takeuchi, M., Lagrangean contact structures on projective cotangent bundles, Osaka J. Math. 31 (1994), 837–860. (1994) Zbl0830.53028MR1315010

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