Killing and Conformal Killing tensors

Abstract

We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of conformal Killing $2$-tensors on Riemannian products of compact manifolds, Weitzenböck formulas leading to non-existence results, and construct various examples of manifolds with conformal Killing tensors.

29 pages; the statement and the proof of Theorem 5.1 have been corrected