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Warped Poisson brackets on warped products
1. | Laboratory of Algebra and Number Theory, Faculté de Mathématiques, USTHB, BP32, El-Alia, 16111 Bab-Ezzouar, Alger, Algeria, Algeria |
2. | Laboratory of Geometry, Analysis, Control and Applications, Université de Saïda, BP138, En-Nasr, 20000 Saïda, Algeria |
References:
[1] |
J. K. Beem, P. E. Ehrlich and Th. G. Powell, Warped product manifolds in relativity, Selected Studies: Physics-astrophysics, mathematics, history of science, pp. 41-56, North-Holland, Amesterdam-New York, 1982. |
[2] |
R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
doi: 10.1090/S0002-9947-1969-0251664-4. |
[3] |
M. Boucetta, Compatibilité des structures pseudo-riemanniennes et des structures de Poisson, C. R. Acad. Sci. Paris, 333 (2001), 763-768.
doi: 10.1016/S0764-4442(01)02132-2. |
[4] |
M. Boucetta, Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras, Differential Geometry and its Applications, 20 (2004), 279-291.
doi: 10.1016/j.difgeo.2003.10.013. |
[5] |
J.-P. Dufour and N. T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, vol. 242, Birkhäuser Verlag, Basel, 2005. |
[6] |
R. L. Fernandes, Connections in Poisson geometry I: Holonomy and invariants, J. Diff. Geom., 54 (2000), 303-365. |
[7] |
E. Hawkins, Noncommutative rigidity, Commun. Math. Phys., 246 (2004), 211-235.
doi: 10.1007/s00220-004-1036-4. |
[8] |
E. Hawkins, The structure of noncommutative deformations, J. Diff. Geom., 77 (2007), 385-424. |
[9] |
R. Nasri and M. Djaa, Sur la courbure des variétés riemanniennes produits, Sciences et Technologie, A-24 (2006), 15-20. |
[10] |
R. Nasri and M. Djaa, On the geometry of the product Riemannian manifold with the Poisson structure, International Electronic Journal of Geometry, 3 (2010), 1-14. |
[11] |
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983. |
[12] |
I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progress in Mathematics, vol. 118, Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8495-2. |
show all references
References:
[1] |
J. K. Beem, P. E. Ehrlich and Th. G. Powell, Warped product manifolds in relativity, Selected Studies: Physics-astrophysics, mathematics, history of science, pp. 41-56, North-Holland, Amesterdam-New York, 1982. |
[2] |
R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
doi: 10.1090/S0002-9947-1969-0251664-4. |
[3] |
M. Boucetta, Compatibilité des structures pseudo-riemanniennes et des structures de Poisson, C. R. Acad. Sci. Paris, 333 (2001), 763-768.
doi: 10.1016/S0764-4442(01)02132-2. |
[4] |
M. Boucetta, Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras, Differential Geometry and its Applications, 20 (2004), 279-291.
doi: 10.1016/j.difgeo.2003.10.013. |
[5] |
J.-P. Dufour and N. T. Zung, Poisson Structures and Their Normal Forms, Progress in Mathematics, vol. 242, Birkhäuser Verlag, Basel, 2005. |
[6] |
R. L. Fernandes, Connections in Poisson geometry I: Holonomy and invariants, J. Diff. Geom., 54 (2000), 303-365. |
[7] |
E. Hawkins, Noncommutative rigidity, Commun. Math. Phys., 246 (2004), 211-235.
doi: 10.1007/s00220-004-1036-4. |
[8] |
E. Hawkins, The structure of noncommutative deformations, J. Diff. Geom., 77 (2007), 385-424. |
[9] |
R. Nasri and M. Djaa, Sur la courbure des variétés riemanniennes produits, Sciences et Technologie, A-24 (2006), 15-20. |
[10] |
R. Nasri and M. Djaa, On the geometry of the product Riemannian manifold with the Poisson structure, International Electronic Journal of Geometry, 3 (2010), 1-14. |
[11] |
B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983. |
[12] |
I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progress in Mathematics, vol. 118, Birkhäuser Verlag, Basel, 1994.
doi: 10.1007/978-3-0348-8495-2. |
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