Hypersurface geometry and Hamiltonian systems of hydrodynamic type (Q1967153)

The paper is an interesting survey on isoparametric hypersurfaces and related areas. In one section the author explains her yet unpublished results on the classification of isoparametric hypersurfaces with six principal curvatures in spheres. Then she explains the connection with integrable dynamical systems, in particular with so called Hamiltonian systems of hydrodynamic type. There is finally a short section on Lie contact structures. For another survey with a different emphasis the reader can also consider the reviewer's contribution in [Handbook of differential geometry. Volume I, pp. 963-995 (2000; Zbl 0979.53003)].