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Combinatorial differential geometry and ideal Bianchi-Ricci identities
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SYSNO ASEP 0362692 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Combinatorial differential geometry and ideal Bianchi-Ricci identities Tvůrce(i) Janyška, J. (CZ)
Markl, Martin (MU-W) RID, SAI, ORCIDZdroj.dok. Advances in Geometry - ISSN 1615-715X
Roč. 11, č. 3 (2011), s. 509-540Poč.str. 32 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova Natural operator ; linear connection ; reduction theorem Vědní obor RIV BA - Obecná matematika CEP GA201/08/0397 GA ČR - Grantová agentura ČR CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000292813700009 EID SCOPUS 79960931455 DOI 10.1515/ADVGEOM.2011.017 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2012
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