On almost polynomial structures from classical linear connections

Anna Bednarska. "On almost polynomial structures from classical linear connections." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 72.1 (2018): null. <http://eudml.org/doc/290763>.

@article{AnnaBednarska2018,
abstract = {Let $\mathcal \{M\}f_m$ be the category of $m$-dimensional manifolds and local diffeomorphisms and let $T$ be the tangent functor on $\mathcal \{M\}f_m$. Let $\mathcal \{V\}$ be the category of real vector spaces and linear maps and let  $\mathcal \{V\}_m$ 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 $F\colon \mathcal \{V\}_m\rightarrow \mathcal \{V\}$ admitting $\mathcal \{M\}f_m$-natural operators $\tilde\{P\}$ transforming classical linear connections $\nabla $ on $m$-dimensional manifolds $M$ into almost polynomial $w$-structures  $\tilde\{P\}(\nabla )$ on $F(T)M=\bigcup _\{x\in M\}F(T_xM)$.},
author = {Anna Bednarska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Classical linear connection; almost polynomial structure; Weil bundle; natural operator},
language = {eng},
number = {1},
pages = {null},
title = {On almost polynomial structures from classical linear connections},
url = {http://eudml.org/doc/290763},
volume = {72},
year = {2018},
}

TY - JOUR
AU - Anna Bednarska
TI - On almost polynomial structures from classical linear connections
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2018
VL - 72
IS - 1
SP - null
AB - Let $\mathcal {M}f_m$ be the category of $m$-dimensional manifolds and local diffeomorphisms and let $T$ be the tangent functor on $\mathcal {M}f_m$. Let $\mathcal {V}$ be the category of real vector spaces and linear maps and let  $\mathcal {V}_m$ 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 $F\colon \mathcal {V}_m\rightarrow \mathcal {V}$ admitting $\mathcal {M}f_m$-natural operators $\tilde{P}$ transforming classical linear connections $\nabla $ on $m$-dimensional manifolds $M$ into almost polynomial $w$-structures  $\tilde{P}(\nabla )$ on $F(T)M=\bigcup _{x\in M}F(T_xM)$.
LA - eng
KW - Classical linear connection; almost polynomial structure; Weil bundle; natural operator
UR - http://eudml.org/doc/290763
ER -