Geodesic
Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case
Archivum mathematicum, Tome 48 (2012) no. 1, pp. 61-80 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper is a continuation of [2], 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.
This paper is a continuation of [2], 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.
DOI : 10.5817/AM2012-1-61
Classification : 20G05, 53C05, 58A32
Keywords: natural operator; linear connection; torsion; reduction theorem; graph 
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Janyška, Josef; Markl, Martin. Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case. Archivum mathematicum, Tome 48 (2012) no. 1, pp. 61-80. doi: 10.5817/AM2012-1-61

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