On almost complex structures from classical linear connections

Jan Kurek, and Włodzimierz M. Mikulski. "On almost complex structures from classical linear connections." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 71.1 (2017): null. <http://eudml.org/doc/289797>.

@article{JanKurek2017,
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. We characterize all regular covariant functors $F:\mathcal \{V\}_m\rightarrow \mathcal \{V\}$ admitting $\mathcal \{M\} f_m$-natural operators $\tilde\{J\}$ transforming classical linear connections $\nabla $ on $m$-dimensional manifolds $M$ into almost complex structures $\tilde\{J\}(\nabla )$ on $F(T)M=\bigcup _\{x\in M\}F(T_xM)$.},
author = {Jan Kurek, Włodzimierz M. Mikulski},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Classical linear connection; almost complex structure; Weil bundle; natural operator},
language = {eng},
number = {1},
pages = {null},
title = {On almost complex structures from classical linear connections},
url = {http://eudml.org/doc/289797},
volume = {71},
year = {2017},
}

TY - JOUR
AU - Jan Kurek
AU - Włodzimierz M. Mikulski
TI - On almost complex structures from classical linear connections
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2017
VL - 71
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. We characterize all regular covariant functors $F:\mathcal {V}_m\rightarrow \mathcal {V}$ admitting $\mathcal {M} f_m$-natural operators $\tilde{J}$ transforming classical linear connections $\nabla $ on $m$-dimensional manifolds $M$ into almost complex structures $\tilde{J}(\nabla )$ on $F(T)M=\bigcup _{x\in M}F(T_xM)$.
LA - eng
KW - Classical linear connection; almost complex structure; Weil bundle; natural operator
UR - http://eudml.org/doc/289797
ER -