The wave equation and separation of variables on the complex sphere S4

E. G. Kalnins, Willard Miller

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)449-469
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume83
Issue number2
DOIs
StatePublished - Oct 1981

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