Hopf surfaces: a family of locally conformal Kaehler metrics and elliptic fibrations

Details Hopf surfaces: a family of locally conformal Kaehler metrics and elliptic fibrations Hopf surfaces: a family of locally conformal Kaehler metrics and elliptic fibrations

1999-07-16

arxiv.org/abs/math/9907105v1

Ann. Mat. Pura Appl. (4) 182 (2003), no. 3, 287--306

Mathematics

Differential Geometry

29 pages

Scientific paper

10.1007/s10231-002-0066-9

We describe a family of locally conformal Kaehler metrics on class 1 Hopf surfaces H containing some recent metrics constructed by P. Gauduchon and L. ornea. We study some canonical foliations associated to these metrics, in particular a 2-dimensional foliation E that is shown to be independent of the metric. We elementary prove that E has compact leaves if and only if H is elliptic. In this case the leaves of E give explicitly the elliptic fibration of H, and the natural orbifold structure on the leaf space is illustrated.

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