Owen Dearricott : Killing tensors on complex and quaternionic projective spaces

A covariant symmetric tensor field is said to be Killing if the symmetrisation of its covariant derivative vanishes. The Killing tensors on standard spheres were classified in the 1980s and are decomposable; namely, they consist of sums of symmetric products of rank 1 Killing tensors dual to Killing fields. Recently, Eastwood proved that the same is true on complex projective space. In this talk we corroborate Eastwood's result by different means. Namely via the Riemannian submersion given by a Hopf fibration and the classical invariant theory of Hermann Weyl. We go on in this vein to classify the Killing tensors on quaternionic projective space to be generated by rank 1 Killing tensors dual to Killing fields and the quadratic Killing tensors found by Matveev and Nikolayevsky in 2024. This is joint work with Yuri Nikolayevsky.