This second edition explores recent progress in the submanifold geometry of space forms,
including new methods based on the holonomy of the normal connection. It contains five …

In this chapter, we give Lie's construction of the space of spheres and define the important
notions of oriented contact and parabolic pencils of spheres. This leads ultimately to a …

Isoparametric hypersurfaces with (g, m) = (6, 2) Page 1 Annals of Mathematics 177 (2013),
53-110 http://dx.doi.Org/10.4007/annals.2013.177.l.2 Isoparametric hypersurfaces with (<7, m) …

We prove, in a purely geometric way, that there are no connected irreducible proper
subgroups of SO (N, 1). Moreover, a weakly irreducible subgroup of SO (N, 1) must either act …

A hypersurface M n− 1 in a real space-form R n, S n or H n is isoparametric if it has constant
principal curvatures. For R n and H n, the classification of isoparametric hypersurfaces is …

Singular Riemannian Foliations and Isoparametric Submanifolds Page 1 Singular Riemannian
Foliations and Isoparametric Submanifolds Gudlaugur Thorbergsson Abstract. We will explain …

Equifocal submanifolds are an extension of the notion of isoparametric submanifolds in
Euclidean spaces to symmetric spaces and consequently they share many of the properties …

Isoparametric hypersurface Mn⊂ Sn+ 1 can be defined as an intersection of the unit sphere
r2=(u1) 2+…+(un+ 2) 2= 1 with the level set F (u)= const of a homogeneous polynomial F of …

We will show how isoparametric submanifolds and polar actions on round spheres lead to
polar foliations and polar actions on compact symmetric spaces and compact Riemannian …

Polar representations and symmetric spaces Page 1 J. reine angew. Math. 507 (1999), 93-106
Journal für die reine und angewandte Mathematik © Walter de Gruyter Berlin • New York …