Separable coordinates for four-dimensional Riemannian spaces

DOI10.1007/BF01611508zbMath0377.53009WikidataQ115393299 ScholiaQ115393299MaRDI QIDQ1246753

Ernest G. Kalnins, Charles P. Boyer

Publication date: 1978

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Local Riemannian geometry (53B20)

Related Items (14)

Nonorthogonal R-separable coordinates for four-dimensional complex Riemannian spaces ⋮ Block-separation of variables: a form of partial separation for natural Hamiltonians ⋮ Some remarkable R-separable coordinate systems for the Helmholtz equation ⋮ Unnamed Item ⋮ Separation of variables in Einstein spaces. II. No ignorable coordinates ⋮ Relativistic fluids and metric symmetries ⋮ Maximal abelian subalgebras of real and complex symplectic Lie algebras ⋮ Nonpolynomial constants of the motion and partial separation of the hamilton—jacobi equation ⋮ Nonorthogonal R-separable coordinates for four-dimensional complex Riemannian spaces ⋮ Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions ⋮ The general theory of R-separation for Helmholtz equations ⋮ Subgroups of Lie groups and separation of variables ⋮ Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces ⋮ Separation of variables and symmetry operators for the conformally invariant Klein-Gordon equation on curved spacetime

Cites Work

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• Separable coordinates for three-dimensional complex Riemannian spaces
• Killing tensors and the separation of the Hamilton-Jacobi equation
• Hamilton-Jacobi and Schrödinger separable solutions of Einstein's equations
• Separation of variables in the Hamilton–Jacobi, Schrödinger, and related equations. I. Complete separation
• Separation of variables in the Hamilton–Jacobi, Schrödinger, and related equations. II. Partial separation
• Separable coordinate systems for the Hamilton-Jacobi, Klein-Gordon and wave equations in curved spaces
• Symmetry and separation of variables for the Hamilton–Jacobi equation W2t−W2x −W2y =0
• Empty space-times with separable Hamilton-Jacobi equation
• R-Separable Coordinates for Three-Dimensional Complex Riemannian Spaces
• R-Separation of Variables for the Four-Dimensional Flat Space Laplace and Hamilton-Jacobi Equations

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