71 research outputs found
A splitting theorem for extremal Kaehler metrics
Based on recent work of S. K. Donaldson and T. Mabuchi, we prove that any
extremal Kaehler metric in the sense of E. Calabi, defined on the product of
polarized compact complex projective manifolds is the product of extremal
Kaehler metrics on each factor, provided that the integral Futaki invariants of
the polarized manifold vanish or its automorphism group satisfies a constraint.
This extends a result of S.-T. Yau about the splitting of a Kaehler-Einstein
metric on the product of compact complex manifolds to the more general setting
of extremal Kaehler metrics
From locally conformally K\"ahler to bi-Hermitian structures on non-K\"ahler complex surfaces
We prove that locally conformally K\"ahler metrics on certain compact complex
surfaces with odd first Betti number can be deformed to new examples of
bi-Hermitian metrics.Comment: minor revision, final versio
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