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Some invariant and equivariant cohomology classes of the space of Kähler metrics. (English) Zbl 1017.53061

In this paper the author defines invariant and equivariant cohomology classes on the space of Kähler forms and discusses relations to the obstructions to existence of Kähler-Einstein metrics and Kähler metrics of harmonic Chern forms. The case of a multiplier Hermitian structure first introduced by Mabuchi and the case of a higher Chern class are considered in details.

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
55N91 Equivariant homology and cohomology in algebraic topology
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