Displaying similar documents to “Characteristic Classes of Flat and of Partially Flat Regular Lie Algebroids over Foliated Manifolds”

The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

Jan Kubarski (2006)

Czechoslovak Mathematical Journal

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This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either ℝ or s l ( 2 , ℝ ) or so ( 3 ) are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to n + 1 , where n is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For ℝ -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...

Affinely equivalent complete flat manifolds

Michal Sadowski (2004)

Open Mathematics

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Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).

Flat semimodules.

Al-Thani, Huda Mohammed J. (2004)

International Journal of Mathematics and Mathematical Sciences

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∇-flat functions on manifolds

Wojciech Kozłowski (2004)

Annales Polonici Mathematici

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We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.