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@article{945951,
author = {Janyška, Josef and Markl, Martin},
article_number = {3},
doi = {http://dx.doi.org/10.1515/advgeom.2011.017},
keywords = {Natural operator; linear connection; reduction theorem; graph},
language = {eng},
issn = {1615-715X},
journal = {Advances in Geometry},
title = {Combinatorial differential geometry and ideal Bianchi–Ricci identities},
url = {http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017.xml?format=INT},
volume = {11},
year = {2011}
}
TY - JOUR
ID - 945951
AU - Janyška, Josef - Markl, Martin
PY - 2011
TI - Combinatorial differential geometry and ideal Bianchi–Ricci identities
JF - Advances in Geometry
VL - 11
IS - 3
SP - 509-540
EP - 509-540
PB - de Gruyter
SN - 1615715X
KW - Natural operator
KW - linear connection
KW - reduction theorem
KW - graph
UR - http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017.xml?format=INT
L2 - http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017.xml?format=INT
N2 - We apply the graph complex approach of~\cite{markl:na} to vector fields depending naturally on a set of vector fields and a linear symmetric connection. We characterize all possible systems of generators for such vector-field valued operators including the classical ones given by normal tensors and covariant derivatives. We also describe the size of the space of such operators and prove the existence of an `ideal' basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi--Ricci identities without the correction terms. The proofs given in this paper combine the classical methods of normal coordinates with the graph complex method.
ER -
JANYŠKA, Josef and Martin MARKL. Combinatorial differential geometry and ideal Bianchi–Ricci identities. \textit{Advances in Geometry}. de Gruyter, 2011, vol.~11, No~3, p.~509-540. ISSN~1615-715X. Available from: https://dx.doi.org/10.1515/advgeom.2011.017.
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