| Title:
|
Remarks on Special Symplectic Connections (English) |
| Author:
|
Panák, Martin |
| Author:
|
Žádník, Vojtěch |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
5 |
| Year:
|
2008 |
| Pages:
|
491-510 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
special symplectic connections |
| Keyword:
|
parabolic contact geometries |
| Keyword:
|
Weyl structures and connections |
| MSC:
|
53B15 |
| MSC:
|
53C15 |
| MSC:
|
53D15 |
| idZBL:
|
Zbl 1212.53113 |
| idMR:
|
MR2501580 |
| . |
| Date available:
|
2009-01-29T09:16:23Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127116 |
| . |
| Reference:
|
[1] Bryant, R.: Bochner–Kähler metrics.J. Amer. Math. Soc. 14 (2) (2001), 623–715. Zbl 1006.53019, MR 1824987, 10.1090/S0894-0347-01-00366-6 |
| Reference:
|
[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. Zbl 1079.53117, MR 2103002 |
| Reference:
|
[3] Cahen, M., Schwachhöfer, L.: Special symplectic connections.eprint arXiv:math/0402221v2. MR 2232865 |
| Reference:
|
[4] Čap, A.: Correspondence spaces and twistor spaces for parabolic geometries.J. Reine Angew. Math. 582 (2005), 143–172. Zbl 1075.53022, MR 2139714, 10.1515/crll.2005.2005.582.143 |
| Reference:
|
[5] Čap, A., Gover, A. R.: Tractor calculi for parabolic geometries.Trans. Amer. Math. Soc. 354 (2002), 1511–1548. Zbl 0997.53016, MR 1873017, 10.1090/S0002-9947-01-02909-9 |
| Reference:
|
[6] Čap, A., Slovák, J.: Parabolic Geometries.to appear in Math. Surveys Monogr., 2008. |
| Reference:
|
[7] Čap, A., Slovák, J.: Weyl Structures for Parabolic Geometries.Math. Scand. 93 (2003), 53–90. Zbl 1076.53029, MR 1997873 |
| Reference:
|
[8] Chu, B. Y.: Symplectic homogeneous space.Trans. Amer. Math. Soc. 197 (1974), 145–159. MR 0342642, 10.1090/S0002-9947-1974-0342642-7 |
| Reference:
|
[9] Fox, D. J.: Contact projective structures.Indiana Univ. Math. J. 54 (6) (2005), 1547–1598. Zbl 1093.53083, MR 2189678 |
| Reference:
|
[10] Jacobowitz, H.: An introduction to CR structures.Math. Surveys Monogr. 32 (1990). Zbl 0712.32001 |
| Reference:
|
[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. Zbl 1162.53324, MR 2462805 |
| Reference:
|
[12] Pikulin, S. V., Tevelev, E. A.: Invariant linear connections on homogeneous symplectic varieties.Transform. Groups 6 (2) (2001), 193–198. Zbl 1009.22014, MR 1835673, 10.1007/BF01597137 |
| Reference:
|
[13] Slovák, J.: Parabolic geometries.Tech. report, IGA preprint 97/11, Univ. of Adelaide, 1997. |
| Reference:
|
[14] Takeuchi, M.: Lagrangean contact structures on projective cotangent bundles.Osaka J. Math. 31 (1994), 837–860. Zbl 0830.53028, MR 1315010 |
| . |
