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 …

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 …

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 Geometric Proof of the Berger Holonomy Theorem Page 1 Annals of Mathematics, 161 (2005),
579-588 A geometric proof of the Berger Holonomy Theorem By CARLOS OLMOS* Dedicated …

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature
vector if the mean curvature vector field H is parallel as a section of the normal bundle …

Minimal Homogeneous Submanifolds in Euclidean Spaces Page 1 Annals of Global
Analysis and Geometry 21: 15–18, 2002. © 2002 Kluwer Academic Publishers. Printed in …

Several classes of irreducible orthogonal representations of compact Lie groups that are of
importance in Differential Geometry have the property that the second osculating spaces of …

We introduce a new integral invariant for isometric actions of compact Lie groups, the
copolarity. Roughly speaking, it measures how far from being polar the action is. We …

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 …