The principal investigator will study the geometry and topology of tight and taut submanifolds. In particular, he will investigate tight submanifolds that are either analytic or orbits of an orthogonal action. Furthermore, the difference between the topology and geometry of two special cases, Dupin and isoparametric hypersurfaces, will be the subject of particular attention. Tight and taut submanifolds are the topological analogues of geometer's minimal surfaces. These in turn are mathematical models for everyday soap films. A soap film, while in the process of being blown is neither tight nor taut. Prior to being blown, the film had both these properties. The principal investigator will solve several mathematics problems which arise from the study of such films.
