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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 a Martin MARKL. Combinatorial differential geometry and ideal Bianchi–Ricci identities. \textit{Advances in Geometry}. de Gruyter, 2011, roč.~11, č.~3, s.~509-540. ISSN~1615-715X. Dostupné z: https://dx.doi.org/10.1515/advgeom.2011.017.
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