Geodesic
The natural operators of general affine connections into general affine connections
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 71 (2017) no. 1

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We reduce the problem of describing all ℳ f_m-natural operators  transforming general affine connections on m-manifolds into general affine ones to the known description of all GL(𝐑^m)-invariant maps 𝐑^m*⊗𝐑^m→⊗^k𝐑^m*⊗⊗ ^k𝐑^m for k=1,3.
Keywords: General affine connection, natural operator 
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Kurek, Jan; Mikulski, Włodzimierz M. The natural operators of general affine connections into general affine connections. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 71 (2017) no. 1. http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a6/

[1] Debecki, J., The natural operators transforming affinors to tensor fields of type (3, 3), Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 39 (2000), 37-49.

[2] Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol. I, J. Wiley-Interscience, New York–London, 1963.

[3] Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry,

[4] Springer-Verlag, Berlin, 1993.