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arXiv · 1301.2483

Spectral properties of a family of minimal tori of revolution in five-dimensional sphere

Mikhail Karpukhin
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Abstract

The normalized eigenvalues $Λ_i(M,g)$ 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 provided.

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Mikhail Karpukhin. 2013-01-11. Spectral properties of a family of minimal tori of revolution in five-dimensional sphere. https://arxiv.org/abs/1301.2483

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