The spectrum and isometric embeddings of surfaces of revolution

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An upper bound on the first S^1 invariant eigenvalue of the Laplacian for invariant metrics on the 2-sphere is used to find obstructions to the existence of isometric embeddings of such metrics in (R^3,can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the surface of revolution cannot be isometrically embedded in (R^3,can). This leads to a generalization of a classical result in the theory of surfaces.
Latex, 11 pages New version contains a new reference and minor stylistic changes

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Differential Geometry, 58G25, 58G30 (Primary) 35P15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/79215

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9910038
 http://arxiv.org/abs/math/9910038

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arXiv