ON STABILITY OF THE FIBRES OF HOPF SURFACES AS HARMONIC MAPS AND MINIMAL SURFACES
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY(2021)
Abstract
We construct a family of Hermitian metrics on the Hopf surface S-3 x S-1, whose fundamental classes represent distinct cohomology classes in the Aeppli cohomology group. These metrics are locally conformally Kahler. Among the toric fibres of pi: S-3 x S-1 -> CP1 two of them are stable minimal surfaces and each of the two has a neighbourhood so that fibres therein are given by stable harmonic maps from 2-torus and outside, far away from the two tori, there are unstable harmonic ones that are also unstable minimal surfaces. A similar result is true for S2n-1 x S-1.
MoreTranslated text
Key words
Stability of harmonic maps, minimal surfaces, Gauduchon metrics, Hopf surfaces
AI Read Science
Must-Reading Tree
Example
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined