Clifford Algebras and New Isoparametric Hypersurfaces

TL;DR

This paper explores the relationship between Clifford algebras and the construction of new isoparametric hypersurfaces, advancing the understanding of geometric structures in differential geometry.

Contribution

It introduces novel methods linking Clifford algebras to the classification and construction of isoparametric hypersurfaces.

Findings

Established new connections between Clifford algebras and hypersurface geometry

Constructed previously unknown classes of isoparametric hypersurfaces

Provided insights into the algebraic structures underlying geometric properties

Abstract

1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: cecil@mathcs.holycross.edu 2. Typed by Wenjiao Yan, School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China. E-mail address: wjyan@mail.bnu.edu.cn