Due to the importance of Killing tensors of rank two in providing quadratic first integrals we point out several algebraic and geometrical features of this class of Killing tensor fields for the two-dimensional Euclidean metric.
"New Properties of Euclidean Killing Tensors of Rank Two." J. Geom. Symmetry Phys. 51 1 - 7, 2019. https://doi.org/10.7546/jgsp-51-2019-1-7