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Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case

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Original title:Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case
Authors:Josef Janyška, Martin Markl
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Original language:English
Field:General mathematics
WWW:link to a new windowhttp://emis.muni.cz/journals/AM/12-1/am2052.pdf
Type:Article in Periodical
Keywords:Natural operator; linear connection; torsion; reduction theorem; graph
Attached files:link to a new windowAM 2012 42 JanMar.pdf

This paper is a continuation of the paper J. Janyška and M. Markl, Combinatorial differential geometry and ideal Bianchi-Ricci identities, Advances in Geometry 11 (2011) 509-540, dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an `ideal' basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi--Ricci identities without corrections.

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