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Connections in regular Poisson manifolds over ℝ-Lie foliations

Jan Kubarski (2000)

Banach Center Publications

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,...

Connections induced by ( 1 , 1 ) -tensor fields on cotangent bundles

Anton Dekrét (1998)

Mathematica Bohemica

On cotangent bundles the Liouville field, the Liouville 1-form ε and the canonical symplectic structure d ε exist. In this paper interactions between these objects and ( 1 , 1 ) -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.

Connections of higher order and product preserving functors

Jacek Gancarzewicz, Noureddine Rahmani, Modesto R. Salgado (2002)

Czechoslovak Mathematical Journal

In this paper we consider a product preserving functor ℱ of order r and a connection Γ of order r on a manifold M . We introduce horizontal lifts of tensor fields and linear connections from M to ℱ ( M ) with respect to Γ . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

Connections with prescribed curvature

Dennis Deturck, Janet Talvacchia (1987)

Annales de l'institut Fourier

We discuss the problem of prescribing the curvature of a connection on a principal bundle whose base manifold is three-dimensional. In particular, we consider the local question: Given a curvature form F , when does there exist locally a connection A such that F is the curvature of A  ? When the structure group of the bundle is semisimple, a finite number of nonlinear identities arise as necessary conditions for local solvability of the curvature equation. We conjecture that these conditions are also...

Curvature properties of a semi-symmetric metric connection on S-manifolds

Mehmet Akif Akyol, Aysel Turgut Vanli, Luis M. Fernández (2013)

Annales Polonici Mathematici

In this study, S-manifolds endowed with a semi-symmetric metric connection naturally related with the S-structure are considered and some curvature properties of such a connection are given. In particular, the conditions of semi-symmetry, Ricci semi-symmetry and Ricci-projective semi-symmetry of this semi-symmetric metric connection are investigated.

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