Carlos Valero

TL;DR: Benenti et al. as discussed by the authors extended the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti.

TL;DR: In this article, the authors classify all orthogonal coordinate systems in M4, allowing complete additively separated solutions of the Hamilton-Jacobi equation for a charged test particle in the Lienard-Wiechert field generated by any possible given motion of a point-charge Q. They also show that only the Cavendish-Coulomb field, corresponding to the uniform motion of Q, admits separation of variables.

TL;DR: In this paper, the theory of orthogonal separation of variables on pseudo-Riemannian manifolds of constant non-zero curvature via concircular tensors and warped products is reviewed and applied simultaneously to both the three-dimensional hyperbolic and de Sitter spaces.

TL;DR: In the context of wave propagation on a manifold X, the characteristic functions are real valued functions on cotangent bundle of X that specify the allowable phase velocities of the waves.

TL;DR: In this paper, the multiplicity sets of first order symbols associated with differential operators on two-dimensional surfaces were studied, inspired by the phenomenon of conical refraction explained by the existence of singularities in the Fresnel hyper surface for Maxwell's equations on an anisotropic crystal.