Clifford systems, algebraically constant second fundamental form and isoparametric hypersurfaces |
| |
Authors: | Sergio Console Carlos Olmos |
| |
Institution: | Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10,?I-10123 Turin, Italy. e-mail: console@dm.unito.it, IT Fa.M.A.F., Universidad Nacional de Córdoba, Ciudad universitaria,?5000 Córdoba, Argentina. e-mail: olmos@mate.uncor.edu, AR
|
| |
Abstract: | In this paper we prove that a submanifold with parallel mean curvature of a space of constant curvature, whose second fundamental
form has the same algebraic type as the one of a symmetric submanifold, is locally symmetric. As an application, using properties
of Clifford systems, we give a short and alternative proof of a result of Cartan asserting that a compact isoparametric hypersurface
of the sphere with three distinct principal curvatures is a tube around the Veronese embedding of the real, complex, quaternionic
or Cayley projective planes.
Received: 22 April 1998 |
| |
Keywords: | Mathematics Subject Classification (1991):53C40 |
本文献已被 SpringerLink 等数据库收录! |
|