On almost polynomial structures from classical linear connections

Anna Bednarska

Anna Bednarska

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 72 (2018), / 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. Let $w$ be a polynomial in one variable with real coefficients. We describe all regular covariant functors $F : 𝒱_{m} \to 𝒱$ admitting $ℳ f_{m}$ -natural operators $\tilde{P}$ transforming classical linear connections $\nabla$ on $m$ -dimensional manifolds $M$ into almost polynomial $w$ -structures $\tilde{P} (\nabla)$ on $F (T) M = ⋃_{x \in M} F (T_{x} M)$ .

Publié le : 2018-01-01
EUDML-ID : urn:eudml:doc:290763

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     author = {Anna Bednarska},
     title = {On almost polynomial structures from classical linear connections},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {72},
     year = {2018},
     language = {en},
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Anna Bednarska. On almost polynomial structures from classical linear connections. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 72 (2018) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2018_72_1_13-18/

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