Geodesic
Algebraic Characterization of Differential Geometric Structures
Serge Skryabin1
1Chebotarev Research Institute, Universitetskaya St. 17, 420008 Kazan, Russia
Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 775-810

See the original article notice from the Heldermann Verlag source

We consider purely algebraic data generalizing the notion of a smooth differentiable manifold. It is given by a triple X, R, W where X is a set, R a commutative associative algebra over the ground field, W a Lie subalgebra and an R-submodule in the derivation algebra of R. Geometric structures studied in differential geometry can be defined on such triples. The main result answers the question about the existence and the uniqueness of an L-invariant unimodular, hamiltonian, contact, or pseudo-riemannian structure in terms of the isotropy subalgebras of points of X. The second major result generalizes a classical fact which says that the Lie algebra of infinitesimal automorphisms of a Riemann metric on a connected manifold is finite dimensional.
Classification: 13N99
Keywords: Unimodular structures, hamiltonian structures, contact structures, Riemann pseudometrics

Serge Skryabin  1

1 Chebotarev Research Institute, Universitetskaya St. 17, 420008 Kazan, Russia 
Serge Skryabin. Algebraic Characterization of Differential Geometric Structures. Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 775-810. http://geodesic.mathdoc.fr/item/JOLT_2008_18_4_a2/
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     title = {Algebraic {Characterization} of {Differential} {Geometric} {Structures}},
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     year = {2008},
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     number = {4},
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