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

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 provided.

References in corpus (2)

• Laplacian eigenvalues functionals and metric deformations on compact manifolds
• Finite-gap minimal Lagrangian surfaces in $C{P}^2$

Cited by in corpus (1)

• Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces