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

Josef Janyška and Martin Markl

Department of Mathematics and Statistics, Masaryk University Kotlářská 2, 611 37 Brno, The Czech Republic
Mathematical Institute of the Academy Žitná 25, 115 67 Prague 1, The Czech Republic


Abstract: 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.

AMSclassification: primary 20G05; secondary 53C05, 58A32.

Keywords: natural operator, linear connection, torsion, reduction theorem, graph.