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

Ryoichi Kobayashi; Kensuke Onda

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arXiv · 0805.1956

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

Ryoichi Kobayashi·Kensuke Onda

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Abstract

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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BibTeX RIS

Ryoichi Kobayashi, Kensuke Onda. 2008-05-14. Moving frames on the twistor space of self-dual positive Einstein 4-manifolds. https://arxiv.org/abs/0805.1956

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