CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

The Spectrum and Isometric Embeddings of Surfaces of Revolution

  Published:2006-06-01
 Printed: Jun 2006
  • Martin Engman
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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 $(\R^3,\can)$. As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in $(\R^3,\can)$. This leads to generalizations of some classical results in the theory of surfaces.
MSC Classifications: 58J50, 58J53, 53C20, 35P15 show english descriptions Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Isospectrality
Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Estimation of eigenvalues, upper and lower bounds
58J50 - Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
58J53 - Isospectrality
53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]
35P15 - Estimation of eigenvalues, upper and lower bounds
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/