Moving frames on the twistor space of self-dual positive Einstein 4-manifolds

Details Moving frames on the twistor space of self-dual positive Einstein 4-manifolds Moving frames on the twistor space of self-dual positive Einstein 4-manifolds

2008-05-14

arxiv.org/abs/0805.1956v1

Mathematics

Differential Geometry

21 pages

Scientific paper

The twistor space of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in 1989. The purpose of this paper is to compare these two families. In particular we compare the Ricci tensor and the behavior under the Ricci flow of these families. As an application, we propose a new proof to the fact that a locally irreducible self-dual positive Einstein 4-manifold is isometric to either $S^4$ with a standard metric or $\PP^2(\C)$ with a Fubini-Study metric.

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