alexa Abstract | Trying to Explicit Proofs of Some Veys Theorems in Linear Connections
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article Open Access

Abstract

Let Χ a diferentiable paracompact manifold. Under the hypothesis of a linear connection r with free torsion Τ on Χ, we are going to give more explicit the proofs done by Vey for constructing a Riemannian structure. We proposed three ways to reach our object. First, we give a sufficient and necessary condition on all of holonomy groups of the connection ∇ to obtain Riemannian structure. Next, in the analytic case of Χ, the existence of a quadratic positive definite form g on the tangent bundle ΤΧ such that it was invariant in the infinitesimal sense by the linear operators ∇k R, where R is the curvature of ∇, shows that the connection ∇ comes from a Riemannian structure. At last, for a simply connected manifold Χ, we give some conditions on the linear envelope of the curvature R to have a Riemannian structure

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Author(s): Lantonirina LS

Keywords

Linear connections, Riemannian connection, Levi-civita connection, Holonomy groups, Linear en-velope, Kth derivations, Lie algebras, Algebra, Combinatorics, Deformations Theory, Geometry, Harmonic Analysis, Homological Algebra, Homotopical Algebra, Latin Squares, Lie Algebra, Lie Superalgebra, Lie Theory, Lie Triple Systems, Loop Algebra, Operad Theory, Quantum Group, Quasi-Group, Representation theory, Super Algebras, Symmetric Spaces, Topologies

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