Generalized Lawson tori and Klein bottles

Abstract

Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces including tori and Klein bottles is extended to a three-parametric family of tori and Klein bottles minimally immersed in spheres. Extremal spectral properties of the metrics on these surfaces are investigated. These metrics include i) both metrics extremal for the first non-trivial eigenvalue on the torus, i.e. the metric on the Clifford torus and the metric on the equilateral torus and ii) the metric maximal for the first non-trivial eigenvalue on the Klein bottle.

17 pages, v.2: minor corrections

References in corpus (5)

• Laplacian eigenvalues functionals and metric deformations on compact manifolds
• Extremal spectral properties of Otsuki tori
• Non-maximality of known extremal metrics on torus and Klein bottle
• Finite-gap minimal Lagrangian surfaces in $C{P}^2$
• Spectral properties of a family of minimal tori of revolution in five-dimensional sphere

Cited by in corpus (3)

• Upper bounds for the first eigenvalue of the Laplacian on non-orientable surfaces
• Index of bipolar surfaces to Otsuki tori
• Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces