The spectrum and isometric embeddings of surfaces of revolution
Differential Geometry
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/9910038,
title = {The spectrum and isometric embeddings of surfaces of revolution},
author = {Martin Engman},
journal= {arXiv preprint arXiv:math/9910038},
year = {2007}
}
Comments
Latex, 11 pages New version contains a new reference and minor stylistic changes