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 …

Problems in submanifold theory have been studied since the invention of calculus and it was
started with differential geometry of plane curves. Owing to his studies of how to draw …

Let M be an isoparametric hypersurface in the sphere S^n with four distinct principal
curvatures. Münzner showed that the four principal curvatures can have at most two distinct …

One of the central problems in Riemannian geometry is to determine how large the classes
of manifolds with positive/nonnegative sectional-, Ricci-or scalar curvature are (see [Gr]). For …

Cohomogeneity one Riemannian G-manifolds (ie Riemannian manifolds with a group G of
isometries having an orbit of codimension one) are studied. A description of such manifolds …

All known examples of isoparametric hypersurfaces of spheres are of the following two
types:¶(1) The homogeneous examples, which are principal orbits of isotropy …

It is well known that Lie groups and homogeneous spaces provide a rich source of
interesting examples for a variety of geometric aspects. Likewise it is often the case that …

arXiv:0707.3091v1 [math.DG] 20 Jul 2007 Page 1 arXiv:0707.3091v1 [math.DG] 20 Jul 2007
NONNEGATIVELY AND POSITIVELY CURVED MANIFOLDS BURKHARD WILKING The aim of …

arXiv:2007.02137v1 [math.DG] 4 Jul 2020 Page 1 arXiv:2007.02137v1 [math.DG] 4 Jul 2020
THE ISOPARAMETRIC STORY, A HERITAGE OF ÉLIE CARTAN QUO-SHIN CHI Abstract. In …

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 …