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Riemann–Poisson manifolds and Ka¨hler–Riemann foliations
- Source :
-
Comptes Rendus. Mathématique . Mar2003, Vol. 336 Issue 5, p423. 6p. - Publication Year :
- 2003
-
Abstract
- Riemann–Poisson manifolds were introduced by the author in C. R. Acad. Sci. Paris, Ser. I 333 (2001) 763–768, and studied in detail in preprint math.DG/0206102. Ka¨hler–Riemann foliations form an interesting subset of the Riemannian foliations with remarkable properties (see Ann. Global Anal. Geom. 21 (2002) 377–399). In this Note we will show that to give a regular Riemann–Poisson structure on a manifold <f>P</f> is equivalent to give a Ka¨hler–Riemann foliation on <f>P</f> such that the leafwise symplectic form is invariant with respect to all local foliation-preserving perpendicular vector fields. Finally, we give some examples of such manifolds. To cite this article: M. Boucetta, C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]
- Subjects :
- *FOLIATIONS (Mathematics)
*POISSON manifolds
*VECTOR fields
Subjects
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 336
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 9402347
- Full Text :
- https://doi.org/10.1016/S1631-073X(03)00079-7