Chern conjecture and isoparametric hypersurfaces

Abstract

In this note we will review the most important results and questions related to Chern conjecture and isoparametric hypersurfaces, as well as their interactions and applications to various aspects in mathematics.

to appear in "Differential Geometry-under the influence of S.S.Chern", edited by Y.B.Shen, Z.M.Shen, S.T.Yau, Higher Education Press and International Press, Beijing-Boston, 2012. arXiv admin note: text overlap with arXiv:0809.1433 by other author

References in corpus (3)

• Normal scalar curvature conjecture and its applications
• Isoparametric and Dupin Hypersurfaces
• Geometry of isoparametric hypersurfaces in Riemannian manifolds

Cited by in corpus (4)

• DDVV-type inequality for skew-symmetric matrices and Simons-type inequality for Riemannian submersions
• Problems related to isoparametric theory
• A lower bound for $L_2$ length of second fundamental form on minimal hypersurfaces
• Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere