It is shown that every orthogonal separable coordinate system for the Helmholtz equation on S4 leads to an R-separable system for the complex wave equation. All orthogonal separable systems on S4 are classified and each is characterized by a commuting triplet of operators from the enveloping algebra of o(5). A consequence of the classification is that the most general cyclidic coordinates for the wave equation arise from ellipsoidal coordinates on S4.
Bibliographical noteFunding Information:
supported by NSF Grant MCS 76-04838 AOI.