The Calabi's metric for the space of Kaehler metrics

Details The Calabi's metric for the space of Kaehler metrics The Calabi's metric for the space of Kaehler metrics

2010-04-30

arxiv.org/abs/1004.5482v1

Mathematics

Differential Geometry

30 pages

Scientific paper

Given any closed Kaehler manifold we define, following an idea by Eugenio Calabi, a Riemannian metric on the space of Kaehler metrics regarded as an infinite dimensional manifold. We prove several geometrical features of the resulting space, some of which we think were already known to Calabi. In particular, the space is a portion of an infinite dimensional sphere and admits explicit unique smooth solutions for the Cauchy and the Dirichlet problems for the geodesic equation.

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