Abstract
We consider the quotient set of the set of nondegenerate affinor fields with respect to the action of the group of nowhere vanishing functions. This set is endowed with a structure of infinite-dimensional Lie group. On this Lie group, we construct an object of linear connection with respect to which all left-invariant vector fields are covariantly constant (the Cartan connection).
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References
M. M. Postnikov, Riemannian Geometry. Semester V (Faktorial, Moscow, 1998).
N. Bourbaki, Lie Groups and Lie Algebras. Lie Algebras, Free Lie Algebras and Lie Groups (Mir, Moscow, 1976).
N. Bourbaki, Differentiable and Analytic Manifolds (Mir, Moscow, 1975).
N. Bourbaki, General Topology. Topological Groups. Numbers and Related Groups and Spaces (Nauka, Moscow, 1969).
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Original Russian Text © E.M. Romanova, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 7, pp. 39–44.
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Romanova, E.M. Manifold of nondegenerate affinor fields. Russ Math. 52, 33–37 (2008). https://doi.org/10.3103/S1066369X08070050
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DOI: https://doi.org/10.3103/S1066369X08070050