Separation of Variables for the Hamilton–Jacobi Equation on Complex Projective Spaces

DOI10.1137/0516006zbMath0569.35012OpenAlexW2077495449MaRDI QIDQ3687076

Ernest G. Kalnins, Charles P. Boyer, Pavel Winternitz

Publication date: 1985

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0516006

zbMATH Keywords

algorithmHamilton-Jacobi equationcomplex projective spaceCasimir operatorsLaplace-Beltrami equationCartan subgroupFubini-Study metricadditive separation of variablesmultiplicative separation of variablesRiemannian Einstein space

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geometric theory, characteristics, transformations in context of PDEs (35A30) Hamilton-Jacobi equations in mechanics (70H20)

Related Items (13)

HUYGENS' PRINCIPLE AND SEPARATION OF VARIABLES ⋮ Are orthogonal separable coordinates really classified? ⋮ Integrable systems based on SU(p,q) homogeneous manifolds ⋮ Abelian integrals and the reduction method for an integrable Hamiltonian system ⋮ Classical superintegrable \(SO(p,q)\) Hamiltonian systems ⋮ Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables ⋮ The Jacobi-Rosochatius problem on an ellipsoid: the Lax representations and billiards ⋮ Equations of motion and wave functions in spherical coordinates for an integrable Hamiltonian system ⋮ Pseudo-orthogonal groups and integrable dynamical systems in two dimensions ⋮ Maximal abelian subalgebras of pseudounitary Lie algebras ⋮ Non-existence of orthogonal coordinates on the complex and quaternionic projective spaces ⋮ Separation coordinates, moduli spaces and Stasheff polytopes ⋮ The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres

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