Mathematics Department, Linkoping University,

Linkoping, SWEDEN

E-mail: bredg@mai.liu.se

**Nondegenerate Killing tensors from conformal Killing
vectors**

**Abstract:**

Koutras has proposed some methods to construct reducible proper conformal
Killing tensors and Killing tensors (which are, in general, irreducible)
when a pair of orthogonal conformal Killing vectors exist in a given space.
We give the completely general result demonstrating that this severe restriction
of orthogonality is unnecessary. In addition we correct and extend some
results concerning Killing tensors constructed from a single conformal
Killing vector. A number of examples demonstrate how it is possible to
construct a much larger class of reducible proper conformal Killing tensors
and Killing tensors than permitted by the Koutras algorithms. In particular,
by showing that all conformal Killing tensors are reducible in conformally
flat spaces, we have a method of constructing all conformal Killing tensors
and hence all the Killing tensors (which will in general be irreducible)
of conformally flat spaces using their conformal Killing vectors.