On lifts of projectable-projectable classical linear connections to the cotangent bundle
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2013)
- Volume: 67, Issue: 1
- ISSN: 0365-1029
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topAnna Bednarska. "On lifts of projectable-projectable classical linear connections to the cotangent bundle." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 67.1 (2013): null. <http://eudml.org/doc/289731>.
@article{AnnaBednarska2013,
abstract = {We describe all $\mathcal \{F\}^2\mathcal \{M\}_\{m_1,m_2,n_1,n_2\}$-natural operators $D\colon Q^\{\tau \}_\{proj-proj\} \rightsquigarrow QT^*$ transforming projectable-projectable classical torsion-free linear connections $\nabla $ on fibred-fibred manifolds $Y$ into classical linear connections $D(\nabla )$ on cotangent bundles $T^*Y$ of $Y$. We show that this problem can be reduced to finding $\mathcal \{F\}^2 \mathcal \{M\}_\{m_1,m_2,n_1,n_2\}$-natural operators $D\colon Q^\{\tau \}_\{proj-proj\}\rightsquigarrow (T^*,\otimes ^pT^*\otimes \otimes ^q T)$ for $p=2$, $q=1$ and $p=3$, $q=0$.},
author = {Anna Bednarska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Fibred-fibred manifold; projectable-projectable linear connection; natural operator.},
language = {eng},
number = {1},
pages = {null},
title = {On lifts of projectable-projectable classical linear connections to the cotangent bundle},
url = {http://eudml.org/doc/289731},
volume = {67},
year = {2013},
}
TY - JOUR
AU - Anna Bednarska
TI - On lifts of projectable-projectable classical linear connections to the cotangent bundle
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2013
VL - 67
IS - 1
SP - null
AB - We describe all $\mathcal {F}^2\mathcal {M}_{m_1,m_2,n_1,n_2}$-natural operators $D\colon Q^{\tau }_{proj-proj} \rightsquigarrow QT^*$ transforming projectable-projectable classical torsion-free linear connections $\nabla $ on fibred-fibred manifolds $Y$ into classical linear connections $D(\nabla )$ on cotangent bundles $T^*Y$ of $Y$. We show that this problem can be reduced to finding $\mathcal {F}^2 \mathcal {M}_{m_1,m_2,n_1,n_2}$-natural operators $D\colon Q^{\tau }_{proj-proj}\rightsquigarrow (T^*,\otimes ^pT^*\otimes \otimes ^q T)$ for $p=2$, $q=1$ and $p=3$, $q=0$.
LA - eng
KW - Fibred-fibred manifold; projectable-projectable linear connection; natural operator.
UR - http://eudml.org/doc/289731
ER -
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