Hopf surfaces: a family of locally conformal Kähler metrics and elliptic fibrations
نویسنده
چکیده
In this paper we describe a family of locally conformal Kähler metrics on class 1 Hopf surfaces Hα,β containing some recent metrics constructed in [GO98]. We study some canonical foliations associated to these metrics, in particular a 2-dimensional foliation Eα,β that is shown to be independent of the metric. We elementary prove that Eα,β has compact leaves if and only if α = β for some integers m and n, namely in the elliptic case. In this case the leaves of Eα,β give explicitly the elliptic fibration of Hα,β , and the natural orbifold structure on the leaf space is illustrated.
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