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3
votes
1
answer
275
views
A (non-Kahler) metric on projectivised vector bundles
Given a hermitian holomorphic vector bundle (E, h) on a complex manifold-with-a-metric (X,g), then consider the following (natural) construction of a metric on the total space of $\mathbb{P}(E)$ : Fir …
2
votes
2
answers
789
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Monge Ampere equations (concavity)
The Monge-Ampere (whether real or complex, whether in a domain or on a manifold) equations usually studied are of the type $F(u, \nabla u, \mathrm{Hess}(u)) = 0$ where $F$ is a concave function of $\m …