Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties

Abstract

Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact Kähler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant Kähler metrics on the total space of $L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat Kähler metric in each Kähler class of $L$.

27 pages

References in corpus (3)

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• A generalised Joyce construction for a family of nonlinear partial differential equations
• Uniqueness among scalar-flat Kähler metrics on non-compact toric $4$-manifolds