ON STABILITY OF THE FIBRES OF HOPF SURFACES AS HARMONIC MAPS AND MINIMAL SURFACES

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.