Compact embedded minimal surfaces in ${\mathbb{S}}^2\times {\mathbb{S}}^1$

Abstract

We prove that closed surfaces of all topological types, except for the non-orientable odd-genus ones, can be minimally embedded in the Riemannian product of a sphere and a circle of arbitrary radius. We illustrate it by obtaining some periodic minimal surfaces in ${\mathbb{S}}^2\times \mathbb{R}$ via conjugate constructions. The resulting surfaces can be seen as the analogy to the Schwarz P-surface in these homogeneous 3-manifolds.

15 pages, 6 figures

References in corpus (2)

• Helicoidal minimal surfaces of prescribed genus, II
• Helicoidal minimal surfaces of prescribed genus, I

Cited by in corpus (3)

• Conjugate Plateau constructions in product spaces
• Genus one minimal k-noids and saddle towers in ${\mathbb{H}}^2\times \mathbb{R}$
• Minimal hypersurfaces in R^n \times S^m