A splitting theorem for equifocal submanifolds with non-flat section

Abstract

In this paper, I prove a splitting theorem for equifocal submanifolds with non-flat section in a simply connected symmetric space of compact type. Also, by using the splitting theorem, I prove that the sections of equifocal submanifolds with non-flat section in an irreducible simply connected symmetric space of compact type are isometric to a sphere or a real projective space.

19pages

References in corpus (2)

• Isoparametric submanifolds and a Chevalley-type restriction theorem
• Singular riemannian foliations with sections, transnormal maps and basic forms