The Dirichlet and the weighted metrics for the space of Kahler metrics

Abstract

In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi metric, the K-energy, the degenerate complex Hessian equation. The second part is on the weighted metrics, for which we investigate as well their geometric properties.

arXiv comment33 pages, new sections on the weighted metrics

References in corpus (1)

• The Calabi's metric for the space of Kaehler metrics

Cited by in corpus (1)

• The Space of Closed $G_2$-Structures. I. Connections