Author(s) :
Luc Vrancken
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 662-2000
MSC 2000
- 53A15 Affine differential geometry
Abstract :
It is well known that locally strongly convex affine hyperspheres
can be determined as solutions of differential euqations of
Monge-Ampere type. In this paper we study in partivular the
3-dimensional case and we assume that the hypersphere admits a
Killing vector field (with respect to the affine metric) whose
integral curves are geodesics with respect to both the induced
affine connection and the Levi Civita connection of the affine
metric. We show that besides the already known examples, such
hyperspheres can be constructed starting from the 2-dimensional
Laplace equation, the 2-dimensional sine-Gordon equation or the
2-dimensional cosh-Gordon equation.