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Embedded constant mean curvature tori in hemispheres of Berger spheres
Abstract
We prove that for all real numbers κ,τ with κ>8τ2 and τ≠ 0, the Berger sphere 𝔼3(κ,τ) contains smooth closed embedded rotational surfaces of genus one with constant mean curvature which are contained in an open hemisphere. This disproves a conjecture of Fernández and Mira. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system, and then verified by the authors.
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BibTeX
@misc{liu2026embedded,
title = {{Embedded constant mean curvature tori in hemispheres of Berger spheres}},
author = {Jihao Liu and Xiang Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23484},
eprint = {2609.23484},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23484},
}
RIS
TY - UNPB
TI - Embedded constant mean curvature tori in hemispheres of Berger spheres
AU - Jihao Liu
AU - Xiang Ma
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23484
UR - https://arxiv.org/abs/2609.23484
AB - We prove that for all real numbers κ,τ with κ>8τ^2 and τ≠ 0, the Berger sphere 𝔼^3(κ,τ) contains smooth closed embedded rotational surfaces of genus one with constant mean curvature which are contained in an open hemisphere. This disproves a conjecture of Fernández and Mira. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system, and then verified by the authors.
ER -