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Constructing equivariant maps for representations

Stefano Francaviglia (2009)

Annales de l’institut Fourier

We show that if Γ is a discrete subgroup of the group of the isometries of ℍ k , and if ρ is a representation of Γ into the group of the isometries of ℍ n , then any ρ -equivariant map F : ℍ k → ℍ n extends to the boundary in a weak sense in the setting of Borel measures. As a consequence of this fact, we obtain an extension of a result of Besson, Courtois and Gallot about the existence of volume non-increasing, equivariant maps. Then, we show that the weak extension we obtain is actually a measurable ρ -equivariant...

Contact manifolds, harmonic curvature tensor and ( k , μ ) -nullity distribution

Basil J. Papantoniou (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field ξ belongs to the ( k , μ ) -nullity distribution. Next it is shown that the dimension of the ( k , μ ) -nullity distribution is equal to one and therefore is spanned by the characteristic vector field ξ .

Continuity of the bending map

Cyril Lecuire (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

The bending map of a hyperbolic 3 -manifold maps a convex cocompact hyperbolic metric on a 3 -manifold with boundary to its bending measured geodesic lamination. As proved in [KeS] and [KaT], this map is continuous. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and show that the quotient map obtained from the bending map is continuous.

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