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Cross ratios, Anosov representations and the energy functional on Teichmüller space

François Labourie (2008)

Annales scientifiques de l'École Normale Supérieure

We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...

CR-submanifolds of locally conformal Kaehler manifolds and Riemannian submersions

Fumio Narita (1996)

Colloquium Mathematicae

We consider a Riemannian submersion π: M → N, where M is a CR-submanifold of a locally conformal Kaehler manifold L with the Lee form ω which is strongly non-Kaehler and N is an almost Hermitian manifold. First, we study some geometric structures of N and the relation between the holomorphic sectional curvatures of L and N. Next, we consider the leaves M of the foliation given by ω = 0 and give a necessary and sufficient condition for M to be a Sasakian manifold.

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