Minicourse on isoparametric hypersurfaces - JAE School 2018 - ICMAT

Notes

• An introduction to isoparametric foliations
  Notes based on a minicourse I gave at Universidade de São Paulo in June 2014, aimed at PhD students. They include a review of the motivation, classical and recent results about isoparametric submanifolds, both in spaces of constant and non-constant curvature.
• The isoparametric story
  Starting with the historial motivation of isoparametric hypersurfaces, these notes by Q. S. Chi contain a thorough discussion of the classification problem of isoparametric hypersurfaces in space forms.
• A survey on isoparametric hypersurfaces and their generalizations
  Although it dates from 2000 and does not contain the recent advances in the area, this article by G. Thorbergsson is probably the most famous survey on isoparametric hypersurfaces and related topics.
• Lie group actions on manifolds
  These notes by J. Berndt contain a summary of the main basic concepts and theorems on Riemannian geometry and Lie group isometric actions.
• Basics of differentiable manifolds
  These notes contain the main very basic notions and results on smooth manifolds.

Books

• T. E. Cecil, P. J. Ryan: Geometry of hypersurfaces, Springer Monographs in Mathematics, Springer, New York, 2015.
• M. M. Alexandrino, R. G. Bettiol: Lie groups and geometric aspects of isometric actions, Springer, Cham, 2015.
• J. Berndt, S. Console, C. Olmos: Submanifolds and holonomy, Second Edition, CRC Press, Boca Raton, FL, 2016.