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Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local equivalence of left-invariant metrics with the same curvature on Lie groups G and G ¯ of dimension three, when G is unimodular and G ¯ is non-unimodular.

Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

Let M be a Riemannian 4-manifold. The associated twistor space is a bundle whose total space Z admits a natural metric. The aim of this article is to study properties of complex structures on Z which are compatible with the fibration and the metric. The results obtained enable us to translate some metric properties on M (scalar flat, scalar-flat Kähler...) in terms of complex properties of its twistor space Z .

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