  A definition is suggested for affine symmetry tensors, which generalize the
notion of affine vectors in the same way that (conformal) Killing tensors
generalize (conformal) Killing vectors. An identity for these tensors is
proved, which gives the second derivative of the tensor in terms of the
curvature tensor, generalizing a well-known identity for affine vectors.
Additionally, the definition leads to a good definition of homothetic tensors.
The inclusion relations between these types of tensors are exhibited. The
relationship between affine symmetry tensors and solutions to the equation of
geodesic deviation is clarified, again extending known results about Killing
tensors.
