On Cartan's Examples of Isoparametric Hypersurfaces and Their Focal Submanifolds
Thomas E. Cecil, Patrick J. Ryan
TL;DR
This survey reviews Cartan's classical examples of isoparametric hypersurfaces in spheres and their focal submanifolds, highlighting historical developments from his foundational work in the late 1930s.
Contribution
It compiles and discusses Cartan's original examples and their significance in the study of isoparametric hypersurfaces, providing historical context and insights.
Findings
Summarizes Cartan's four key papers from 1938-1940.
Highlights the structure of Cartan's isoparametric hypersurfaces.
Discusses the properties of focal submanifolds associated with these hypersurfaces.
Abstract
This paper is a survey of Cartan's examples of isoparametric hypersurfaces in spheres and their focal submanifolds that were described in his fundamental work on the subject, which appeared in four papers published during the period 1938-1940.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds