5 problems

Let $(M,\mathbf g)$ be a pseudo-Riemannian space of constant curvature, let $I(M)$ be its isometry group, and let $i(M)$ be the Lie algebra of $I(M)$ generated by Killing vector fi…

Let $g$ be a metric, let $L$ be a 1-form, and let $D_g^L$ be the deformed prolongation connection whose parallel sections correspond to solutions of the relative Killing-tensor equ…

Let $(E_p)$ denote the differential equation considered in Chapter 4 of Gallot's paper, and let a symmetric Killing tensor of valence $p$ mean a symmetric $p$-tensor whose complete…

Diagonalisation conjecture. Under the action of the isometry group, any integrable Killing tensor on $S^n$ is equivalent to one with a diagonal algebraic curvature tensor.

A stationary axisymmetric vacuum spacetime is a spacetime admitting a stationary and axisymmetric metric satisfying the vacuum Einstein equations. A rank-four Killing tensor is a s…