Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere Sn and Euclidean n-space Rn

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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-10-31T01:27:12Z
dc.date.available2008-10-31T01:27:12Z
dc.date.issued1986-07
dc.description.abstractThe following problem is solved: What are all the ``different'' separable coordinate systems for the Laplace–Beltrami eigenvalue equation on the n-sphere Sn and Euclidean n-space Rn and how are they constructed? This is achieved through a combination of differential geometric and group theoretic methods. A graphical procedure for construction of these systems is developed that generalizes Vilenkin's construction of polyspherical coordinates. The significance of these results for exactly soluble dynamical systems on these manifolds is pointed out. The results are also of importance for the analysis of the special functions appearing in the separable solutions of the Laplace–Beltrami eigenvalue equation on these manifolds.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationKalnins, E.G. & Miller, W., Jr. (1986). Separation of variables on n-dimensional Riemannian manifolds. I. The n-sphere Sn and Euclidean n-space Rn. Journal of Mathematical Physics, 27, 1721.en_US
dc.identifier.doi10.1063/1.527088en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1219
dc.language.isoen
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/27/1721/1en_US
dc.rightsCopyright 1986 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectRiemann spaceen_US
dc.subjectEuclidean spaceen_US
dc.subjectmathematical manifoldsen_US
dc.subjectcoordinatesen_US
dc.subjectdifferential geometryen_US
dc.subjectdynamical systemsen_US
dc.subjectkilling vectorsen_US
dc.subjecttensorsen_US
dc.subjectHamilton&minusen_US
dc.subjectJacobi equationsen_US
dc.subjectanalytical solutionen_US
dc.subjectdifferential equationsen_US
dc.titleSeparation of variables on n-dimensional Riemannian manifolds. I. The n-sphere Sn and Euclidean n-space Rnen_US
dc.typeJournal Articleen_US
pubs.begin-page1721en_NZ
pubs.elements-id84079
pubs.end-page1736en_NZ
pubs.issue7en_NZ
pubs.volume27en_NZ
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