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Combinatorial differential geometry and ideal Bianchi-Ricci identities
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SYSNO ASEP 0362692 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Combinatorial differential geometry and ideal Bianchi-Ricci identities Author(s) Janyška, J. (CZ)
Markl, Martin (MU-W) RID, SAI, ORCIDSource Title Advances in Geometry - ISSN 1615-715X
Roč. 11, č. 3 (2011), s. 509-540Number of pages 32 s. Language eng - English Country DE - Germany Keywords Natural operator ; linear connection ; reduction theorem Subject RIV BA - General Mathematics R&D Projects GA201/08/0397 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000292813700009 EID SCOPUS 79960931455 DOI 10.1515/ADVGEOM.2011.017 Annotation We apply the graph complex approach of [8] 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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