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 …

A subset S of a Riemannian manifold N is called extrinsically homogeneous if S is an orbit of
a subgroup of the isometry group of N. In [Th], Thorbergsson proved the remarkable result …

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 …

In this paper, as a suitable application of the well-known generalized maximum principle of
Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces …

In [4] it was proved that given a submanifold of Euclidean space the representation on the
normal space of the holonomy group of the normal connection is an^-representation (ie …

A suhma~ ifold M of euclidean space is called eztrinsic symmetric if it is invariant under the
reflection at each afflne normal space p+ upM, p 6 M. In particular M with its induced metric …

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 …

Abstract Let Mn, n> 2, be an orbit of a representation of a compact Lie group which is
irreducible and full as a submanifold of the ambient space. We prove that if M admits a …

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 …

We study the (restricted) holonomy group Holšr? Ž of the normal connection r?(shortened to
normal holonomy group) of a K€ ahler submanifold of a complex space form. We prove that …