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On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles. (English) Zbl 0968.53050
The author considers a Riemannian metric and a functional (named modified Mabuchi functional) for a class of Kähler metrics, and he proves that, for any two Kähler metrics, there exists a geodesic connecting them. The relation between the extremal metrics and a lower bound of the modified Mabuchi functional is studied.
Reviewer: A.Neagu (Iaşi)

53C55 Global differential geometry of Hermitian and Kählerian manifolds
58D17 Manifolds of metrics (especially Riemannian)
58E11 Critical metrics
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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