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On conformally flat Lorentz parabolic manifolds

Yoshinobu Kamishima (2014)

Open Mathematics

We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.

On rank one symmetric space

Inkang Kim (2004/2005)

Séminaire de théorie spectrale et géométrie

In this paper we survey some recent results on rank one symmetric space.

On the asymptotic geometry of gravitational instantons

Vincent Minerbe (2010)

Annales scientifiques de l'École Normale Supérieure

We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.

On the holonomy of Lorentzian metrics

Charles Boubel (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Indecomposable Lorentzian holonomy algebras, except 𝔰𝔬 ( n , 1 ) and { 0 } , are not semi-simple; they possibly belong to four families of algebras. All four families are realized as families of holonomy algebras: we describe the corresponding set of germs of metrics in each case.

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