Curvature properties of submanifolds
The focal set of a submanifold of Euclidean space is the generalisation of the set of
centres of curvature of a plane curve. There is a strong link between
properties of this focal set and the geometry and topology of the submanifold.
This group investigates these links. Currently we are investigating the
existence of parallel submanifolds which all have the same focal set but which are
embedded in different ways. We are also interested in generalising
results about tight, taut, isoparametric and Chen submanifolds of Euclidean space
to submanifolds of other spaces such as spheres or symmetric spaces.