Symplectic connections with parallel Ricci tensor

Michel Cahen; Simone Gutt; John Rawnsley

Banach Center Publications (2000)

  • Volume: 51, Issue: 1, page 31-41
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Cahen, Michel, Gutt, Simone, and Rawnsley, John. "Symplectic connections with parallel Ricci tensor." Banach Center Publications 51.1 (2000): 31-41. <http://eudml.org/doc/209041>.

@article{Cahen2000,
abstract = {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.},
author = {Cahen, Michel, Gutt, Simone, Rawnsley, John},
journal = {Banach Center Publications},
keywords = {symplectic connection; Kähler manifold; Ricci tensor; Jordan form; parallel endomorphism},
language = {eng},
number = {1},
pages = {31-41},
title = {Symplectic connections with parallel Ricci tensor},
url = {http://eudml.org/doc/209041},
volume = {51},
year = {2000},
}

TY - JOUR
AU - Cahen, Michel
AU - Gutt, Simone
AU - Rawnsley, John
TI - Symplectic connections with parallel Ricci tensor
JO - Banach Center Publications
PY - 2000
VL - 51
IS - 1
SP - 31
EP - 41
AB - 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.
LA - eng
KW - symplectic connection; Kähler manifold; Ricci tensor; Jordan form; parallel endomorphism
UR - http://eudml.org/doc/209041
ER -

References

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  1. [1] A. Besse, Einstein Manifolds, Springer, 1986. Zbl1147.53001
  2. [2] P. Bieliavsky, Espaces symétriques symplectiques, thèse de doctorat, Université Libre de Bruxelles, 1995. 
  3. [3] F. Bourgeois and M. Cahen, A variational principle for symplectic connections, J. Geometry and Physics, (sous presse). Zbl0963.53050
  4. [4] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. II, Interscience Publ., 1969. Einstein Manifolds, Springer, 1986. Zbl0175.48504
  5. [5] A. Lichnerowicz, Quantum mechanics and deformations of geometrical dynamics, in: Quantum theory, groups, fields and particles, Reidel, 1983, 3-82. 
  6. [6] O. Loos, Symmetric Spaces, Benjamin, 1969. 
  7. [7] I. Vaisman, Symplectic curvature tensors, Monatshefte Math. 100 (1985), 299-327. Zbl0571.53025
  8. [8] H. Wu, Holonomy groups of indefinite metrics, Pac. J. Math. 20 (1967), 351-392. Zbl0149.39603

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