- 99-41 M.L. Bialy, Tel-Aviv University
- Rigidity for periodic magnetic fields.
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Feb 2, 99
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Abstract. We study the motion of a charge on a conformally flat
Riemannian torus in the presence of magnetic
field. We prove that for any non-zero magnetic field
there always exist orbits of this motion which have conjugate
points. We conjecture that the restriction of conformal flatness
of the metric is
not essential for this result. This would provide a ``twisted''
version of the recent generalisation of Hopf's rigidity result
obtained by Burago and Ivanov.