The spectrum and isometric embeddings of surfaces of revolution

Details The spectrum and isometric embeddings of surfaces of revolution The spectrum and isometric embeddings of surfaces of revolution

1999-10-07

arxiv.org/abs/math/9910038v2

Mathematics

Differential Geometry

Latex, 11 pages New version contains a new reference and minor stylistic changes

Scientific paper

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.

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