Geodesic
The Spectrum and Isometric Embeddings of Surfaces of Revolution
Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 226-236

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DOI

A sharp upper bound on the first ${{S}^{1}}$ invariant eigenvalue of the Laplacian for ${{S}^{1}}$ invariant metrics on ${{S}^{2}}$ is used to find obstructions to the existence of ${{S}^{1}}$ equivariant isometric embeddings of such metrics in ( ${{\mathbb{R}}^{3}}$ , can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in ( ${{\mathbb{R}}^{3}}$ , can). This leads to generalizations of some classical results in the theory of surfaces.
DOI : 10.4153/CMB-2006-023-7
Mots-clés : 58J50, 58J53, 53C20, 35P15 
Engman, Martin. The Spectrum and Isometric Embeddings of Surfaces of Revolution. Canadian mathematical bulletin, Tome 49 (2006) no. 2, pp. 226-236. doi: 10.4153/CMB-2006-023-7
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     title = {The {Spectrum} and {Isometric} {Embeddings} of {Surfaces} of {Revolution}},
     journal = {Canadian mathematical bulletin},
     pages = {226--236},
     year = {2006},
     volume = {49},
     number = {2},
     doi = {10.4153/CMB-2006-023-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2006-023-7/}
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