Abstract
We consider the quotient manifold of the manifold of nondegenerate affinor fields on a compact manifold with respect to the action of the group of nowhere vanishing functions. On this manifold, we construct a Cartan connection and find its torsion tensor. We also find the geodesics of the Cartan connection.
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References
M. M. Postnikov, Riemannian Geometry. Lectures on Geometry. Semester V (Faktorial, Moscow, 1998) [in Russian].
E.M. Romanova, “Manifold of Nondegenerate Affinor Fields” Izv. Vyssh.Uchebn. Zaved.Mat., No. 7, 39–45 (2008) [Russian Mathematics (Iz. VUZ) 52 (7), 33–37, (2008)].
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Original Russian Text © E.M. Romanova, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 5, pp. 68–72.
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Romanova, E.M. Cartan connection and its geodesics on a manifold of nondegenerate affinor fields. Russ Math. 53, 59–62 (2009). https://doi.org/10.3103/S1066369X09050089
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DOI: https://doi.org/10.3103/S1066369X09050089