The Space of Kähler metrics (II)
| dc.creator | Calabi, E. | |
| dc.creator | Chen, X. X. | |
| dc.date | 2001-08-23 | |
| dc.date.accessioned | 2026-07-07T04:43:06Z | |
| dc.date.available | 2026-07-07T04:43:06Z | |
| dc.description | This paper, the second of a series, deals with the function space of all smooth Kähler metrics in any given closed complex manifold $M$ in a fixed cohomology class. The previous result of the second author \cite{chen991} showed that the space is a path length space and it is geodesically convex in the sense that any two points are joined by a unique path, which is always length minimizing and of class C^{1,1}. This already confirms one of Donaldson's conjecture completely and verifies another one partially. In the present paper, we show first of all, that the space is, as expected, a path length space of non-positive curvature in the sense of A. D. Alexanderov. The second result is related to the theory of extremal Kähler metrics, namely that the gradient flow of the K energy is strictly length decreasing on all paths except those induced by a path of holomorphic automorphisms of $M$. This result, in particular, implies that extremal Kähler metric is unique up to holomorphic transformations, provided that Donaldson's conjecture on the regularity of geodesic is true. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0108162 | |
| dc.identifier | http://arxiv.org/abs/math/0108162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62071 | |
| dc.subject | Differential Geometry | |
| dc.title | The Space of Kähler metrics (II) | |
| dc.type | text |