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Papers - Hopf surfaces | |
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Hopf surfaces: locally conformal Kähler metrics and foliations
Abstract
In this paper I describe a family of locally conformal Kähler metrics
on class 1 Hopf surfaces. By studying some canonical foliations
associated to these metrics, in particular a 2-dimensional foliation
Eα,β that is shown to be independent of the metric, I
prove with
elementary tools
that Eα,β has compact leaves
if and only if αm=βn
for some integers m and n, namely in the
elliptic case. In this case I prove that the leaves of
Eα,β
give explicitly the elliptic fibration, and describe
the natural orbifold
structure on the leaf space.
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