Combinatorial differential geometry and ideal Bianchi-Ricci identities   II - the torsion case
  This paper is a continuation of arXiv:0809.1158, 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. 
Josef Jany\v{s}ka, Martin Markl
math.DG