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Connections in regular Poisson manifolds over ℝ-Lie foliations

100%

Kubarski J.

Banach Center Publications

2000

tom 51

nr 1

141-149

The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally, F has compact leaves (then F is a fibration over $S^{1}$), an analogue of the Euler-Poincaré-Hopf index theorem for flat connections with singularities along closed transversals is obtained.

Integrable systems and group actions

86%

Miranda E.

Open Mathematics

2014

tom 12

nr 2

240-270

The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.

Ograniczanie wyników

1 Banach Center Publications

1 Open Mathematics

1 Kubarski J.

1 Miranda E.

1 2014

1 2000

Wyniki wyszukiwania

Connections in regular Poisson manifolds over ℝ-Lie foliations

Integrable systems and group actions