Geodesic
On almost complex structures from classical linear connections
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1.

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Let ℳ f_m be the category of m-dimensional manifolds and local diffeomorphisms and  let T be the tangent functor on ℳ f_m. Let 𝒱 be the category of real vector spaces and linear maps and let 𝒱_m be the category of m-dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors F:𝒱_m→𝒱 admitting ℳ f_m-natural operators J̃ transforming classical linear connections ∇ on m-dimensional manifolds M into almost complex structures J̃(∇) on F(T)M=⋃_x∈ MF(T_xM).
Keywords: Classical linear connection, almost complex structure, Weil bundle, natural operator 
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Kurek, Jan; Mikulski, Włodzimierz M. On almost complex structures from classical linear connections. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1. http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a4/

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