Spectral properties of bipolar surfaces to Otsuki tori

Abstract

The $i$-th eigenvalue ${\lambda }_i$ of the Laplace–Beltrami operator on a surface can be considered as a functional on the space of all Riemannian metrics of unit volume on this surface. Surprisingly only few examples of extremal metrics for these functionals are known. In the present paper a new countable family of extremal metrics on the torus is provided.