Symplectic connections with parallel Ricci tensor

• Autorzy: Michel Cahen , Simone Gutt , John Rawnsley
• Języki publikacji: EN

Abstrakty

EN

A variational principle introduced to select some symplectic connections leads to field equations which, in the case of the Levi Civita connection of Kähler manifolds, are equivalent to the condition that the Ricci tensor is parallel. This condition, which is stronger than the field equations, is studied in a purely symplectic framework.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2000
• Tom: 51
• Numer: 1
• Strony: 31-41

Daty

wydano

2000

Twórcy

autor

Michel Cahen

• Université Libre de Bruxelles, Campus Plaine, CP 218, Bvd du Triomphe, 1050 Brussels, Belgium

autor

Simone Gutt

• Université Libre de Bruxelles, Campus Plaine, CP 218, Bvd du Triomphe, 1050 Brussels, Belgium

autor

John Rawnsley

• Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

Bibliografia

• [1] A. Besse, Einstein Manifolds, Springer, 1986.
• [2] P. Bieliavsky, Espaces symétriques symplectiques, thèse de doctorat, Université Libre de Bruxelles, 1995.
• [3] F. Bourgeois and M. Cahen, A variational principle for symplectic connections, J. Geometry and Physics, (sous presse).
• [4] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. II, Interscience Publ., 1969. Einstein Manifolds, Springer, 1986.
• [5] A. Lichnerowicz, Quantum mechanics and deformations of geometrical dynamics, in: Quantum theory, groups, fields and particles, Reidel, 1983, 3-82.
• [6] O. Loos, Symmetric Spaces, Benjamin, 1969.
• [7] I. Vaisman, Symplectic curvature tensors, Monatshefte Math. 100 (1985), 299-327.
• [8] H. Wu, Holonomy groups of indefinite metrics, Pac. J. Math. 20 (1967), 351-392.