The principal investigator will study isoparametric submanifolds of Riemannian manifolds. A submanifold of Euclidean space is isoparametric if its normal bundle is flat and the principal curvatures along any locally defined normal vector field are constant. The research will use topological methods to construct new examples of isoparametric submanifolds in the finite and infinite dimensional case. This research in a classical area of differential geometry attempts to explain and classify ways in which manifolds or surfaces sit inside space. In particular, the research will consider families of surfaces which fill space in layers which are curved in a fixed way. Such surfaces appear, for example, as layers in composite materials. The methods to be used in the study come from a wide range of areas such as algebraic topology and group theory.
