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

Published online by Cambridge University Press:  20 November 2018

Mikhail Karpukhin
Mikhail Karpukhin*
Affiliation:
Department of Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, GSP-1, 119991, Moscow, Russia. e-mail: mikhail.karpukhin@gmail.com Independent University of Moscow, Bolshoy Vlasyevskiy pereulok 11, 11902, Moscow, Russia
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Abstract

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The normalized eigenvalues ${{\Lambda }_{i}}\left( M,\,g \right)$ 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 this paper a family of extremal metrics induced by minimal immersions in ${{\mathbb{S}}^{5}}$ is investigated.

Keywords

58J50Extremal metricminimal surface

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 2 , 01 June 2015 , pp. 285 - 296
Copyright
Copyright © Canadian Mathematical Society 2015

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