  When spacetime torsion is present, geodesics and autoparallels generically do
not coincide. In this work, the well-known method that uses Killing vectors to
solve the geodesic equations is generalized for autoparallels. The main
definition is that of T-Killing vectors: vector fields such that, when their
index is lowered with the metric, have vanishing symmetric derivative when
acted with a torsionfull and metric-compatible derivative. The main property of
T-Killing vectors is that their contraction with the autoparallels' tangents
are constant along these curves. As an example, in a static and spherically
symmetric situation, the autoparallel equations are reduced to an effective
one-dimensional problem. Other interesting properties and extensions of
T-Killing vectors are discussed.
