Flat Conformal Structure Research Articles

Bending and stamping deformations of hyperbolic manifolds

The paper deals with some geometric approaches (from the viewpoint of (n + 1)- dimentional Lobachevsky geometry) to the deformation theory for uniformized conformal (i.e., flat conformal) structures on a hyperbolic n-manifold M with finite volume. Namely, two kinds of deformations are studied: bendings and stampings along totally geodesic submanifolds of M. The construction of the last deformation disproves a conjecture of C. Kourouniotis.