The Calabi functional on a ruled surface

Details The Calabi functional on a ruled surface The Calabi functional on a ruled surface

2007-03-19

arxiv.org/abs/math/0703562v1

Ann. Sci. \'Ec. Norm. Sup\'er. 42 (2009), 837--856

Mathematics

Differential Geometry

23 pages, 3 figures

Scientific paper

We study the Calabi functional on a ruled surface over a genus two curve. For
polarisations which do not admit an extremal metric we describe the behaviour
of a minimising sequence splitting the manifold into pieces. We also show that
the Calabi flow starting from a metric with suitable symmetry gives such a
minimising sequence.

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