Kalnins, E. G., & Miller, W., Jr. (1980). Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations. SIAM Journal on Mathematical Analysis, 11(6), 1011–1026. https://doi.org/10.1137/0511089
Permanent Research Commons link: https://hdl.handle.net/10289/12373
Every separable coordinate system for the Hamilton-Jacobi equation on a Riemannian manifold Vₙ corresponds to a family of n-1 Killing tensors in involution, but the converse is false. For general n we find a practical characterization of those involutive families of Killing tensors that correspond to variable separation, orthogonal or not.
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