On almost complex structures from classical linear connections

Jan Kurek; Włodzimierz M. Mikulski

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017), / Harvested from The Polish Digital Mathematics Library

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Résumé

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 $F : 𝒱_{m} \to 𝒱$ admitting $ℳ f_{m}$ -natural operators $\tilde{J}$ transforming classical linear connections $\nabla$ on $m$ -dimensional manifolds $M$ into almost complex structures $\tilde{J} (\nabla)$ on $F (T) M = ⋃_{x \in M} F (T_{x} M)$ .

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:289797

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     title = {On almost complex structures from classical linear connections},
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     year = {2017},
     language = {en},
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Jan Kurek; Włodzimierz M. Mikulski. On almost complex structures from classical linear connections. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_55/

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