|
AHS-structures and affine holonomies
Author(s):
Andreas
Cap
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1073-1080.
MSC (2000):
Primary 53C29, 53C10;
Secondary 53C15, 53C30, 53B15
Posted:
October 22, 2008
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that a large class of non-metric, non-symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS-structures on certain generalized flag manifolds.
References:
-
- 1.
- M. Berger, Sur les groupes d'holonomie homogène des variétés à connexion affine et des variétés riemanniennes. Bull. Soc. Math. France 83 (1955), 279-330. MR 0079806 (18:149a)
- 2.
- M. Cahen, L.J. Schwachhöfer, special symplectic connections, preprint, math.DG/0402221
- 3.
- A. Čap, H. Schichl, Parabolic geometries and canonical Cartan connections. Hokkaido Math. J. 29, no. 3 (2000), 453-505. MR 1795487 (2002f:53036)
- 4.
- A. Čap, J. Slovák, Weyl structures for parabolic geometries. Math. Scand. 93, 1 (2003), 53-90. MR 1997873 (2004j:53065)
- 5.
- A. Čap, J. Slovák, V. Souček, Invariant operators on manifolds with almost Hermitian symmetric structures, II. Normal Cartan connections. Acta Math. Univ. Comenian. 66 (1997), 203-220. MR 1620484 (2000a:53045)
- 6.
- S. Kobayashi, T. Nagano, On filtered Lie algebras and geometric structures, I, II. J. Math. Mech. 13 (1964), 875-907; J. Math. Mech. 14 (1965), 513-521. MR 0168704 (29:5961); MR 0185042 (32:2512)
- 7.
- S.A. Merkulov, L.J. Schwachhöfer, Classification of irreducible holonomies of torsion-free affine connections. Ann. Math. 150 (1999) 77-149; Addendum: Ann. Math. 150 (1999) 1177-1179. MR 1715321 (2000m:53065a); MR 1740981 (2000m:53065b)
- 8.
- K. Yamaguchi, Differential systems associated with simple graded Lie algebras. Adv. Stud. Pure Math. 22 (1993), 413-494. MR 1274961 (95g:58263)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
53C29, 53C10,
53C15, 53C30, 53B15
Retrieve articles in all Journals with MSC
(2000):
53C29, 53C10,
53C15, 53C30, 53B15
Additional Information:
Andreas
Cap
Affiliation:
Institut für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria - and - International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien, Austria
Email:
Andreas.Cap@esi.ac.at
DOI:
10.1090/S0002-9939-08-09722-0
PII:
S 0002-9939(08)09722-0
Received by editor(s):
April 22, 2008
Posted:
October 22, 2008
Additional Notes:
The author was supported by project P 19500-N13 of the ``Fonds zur Förderung de wissenschaftlichen Forschung'' (FWF)
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org