Convergence of Bergman geodesics on CP^1

Abstract

The space of positively curved hermitian metrics on a positive holomorphic line bundle over a compact complex manifold is an infinite-dimensional symmetric space. It is shown by Phong and Sturm that geodesics in this space can be uniformly approximated by geodesics in the finite dimensional spaces of Bergman metrics. We prove a stronger C^2-approximation in the special case of toric (i.e. S^1-invariant) metrics on CP^1.

23 pages

References in corpus (3)

• Bergman metrics and geodesics in the space of Kähler metrics on toric varieties
• Partition function zeros at first-order phase transitions: A general analysis
• Positivity of direct image bundles and convexity on the space of Kahler metrics

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• A Wess--Zumino--Witten type equation in the space of Kähler potentials in terms of Hermitian--Yang--Mills metrics
• Toric partial density functions and stability of toric varieties