Počet záznamů: 1

Combinatorial differential geometry and ideal Bianchi-Ricci identities

  1. 1.
    0362692 - MU-W 2012 RIV DE eng J - Článek v odborném periodiku
    Janyška, J. - Markl, Martin
    Combinatorial differential geometry and ideal Bianchi-Ricci identities.
    Advances in Geometry. Roč. 11, č. 3 (2011), s. 509-540 ISSN 1615-715X
    Grant CEP: GA ČR GA201/08/0397
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: Natural operator * linear connection * reduction theorem
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.338, rok: 2011
    http://www.degruyter.com/view/j/advg.2011.11.issue-3/advgeom.2011.017/advgeom.2011.017.xml

    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.
    Trvalý link: http://hdl.handle.net/11104/0198945
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