Displaying similar documents to “A Singularity Theorem for Twistor Spinors”

The positive mass theorem for ALE manifolds

Mattias Dahl (1997)

Banach Center Publications

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We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.

Quaternionic contact structures in dimension 7

David Duchemin (2006)

Annales de l’institut Fourier

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The conformal infinity of a quaternionic-Kähler metric on a 4 n -manifold with boundary is a codimension 3 distribution on the boundary called quaternionic contact. In dimensions 4 n - 1 greater than 7 , a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7 , we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic-Kähler metric. This allows us to find the quaternionic-contact...

Compatible complex structures on twistor space

Guillaume Deschamps (2011)

Annales de l’institut Fourier

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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 .

Monopole metrics and the orbifold Yamabe problem

Jeff A. Viaclovsky (2010)

Annales de l’institut Fourier

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We consider the self-dual conformal classes on n # ℂℙ 2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3 -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact...