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Spectral Properties of a Family of Minimal Tori of Revolution in Five-dimensional Sphere

  Published:2015-03-11
 Printed: Jun 2015
  • Mikhail Karpukhin,
    Department of Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, GSP-1, 119991, Moscow, Russia
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Abstract

The normalized eigenvalues $\Lambda_i(M,g)$ of the Laplace-Beltrami operator can be considered as functionals on the space of all Riemannian metrics $g$ on a fixed surface $M$. In recent papers several explicit examples of extremal metrics were provided. These metrics are induced by minimal immersions of surfaces in $\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family of extremal metrics induced by minimal immersions in $\mathbb{S}^5$ is investigated.
Keywords: extremal metric, minimal surface extremal metric, minimal surface
MSC Classifications: 58J50 show english descriptions Spectral problems; spectral geometry; scattering theory [See also 35Pxx] 58J50 - Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
 

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