Generalized symplectic structure on the bundle of connections

Authors
Lopez, MC Masque, JM
Citation
Mc. Lopez et Jm. Masque, Generalized symplectic structure on the bundle of connections, CR AC S I, 328(1), 1999, pp. 41-44
Citations number
6
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
328
Issue
1
Year of publication
1999
Pages
41 - 44
Database
ISI
SICI code
0764-4442(199901)328:1<41:GSSOTB>2.0.ZU;2-J
Abstract
We prove that on the bundle of connections of an arbitrary principal bundle pi : P --> M there exists a canonical differential 2-form taking values in the adjoint bundle pi(g) : adP --> M which defines a generalized symplecti c structure and which verifies a property of "universal curvature". The res ults of the present Note generalize those of [3] to an arbitrary Lie group. (C) Academie des Sciences/Elsevier, Paris.