Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case
|Original title:||Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case|
|Authors:||Josef Janyška, Martin Markl|
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.