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 …

We will classify the homogeneous spaces M= G/K satisfying that (i) M are fibered over
irreducible symmetric spaces G/H, and (ii) certain G-invariant metrics on G/K are go with …

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 [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 …

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 …

In this paper we consider the parallel translations of the normal bundles of the orbits of
Hermann actions on compact symmetric spaces and represent such parallel translations by …

The local orbit types of symmetric spaces under the actions of the isotropy subgroups Page
1 Diftercntial Geometry and its Applications II (1999) 29-38 North-Holland www.cl~evicr.comllocate/dit&o …

In 1980, Oniščik [AL Oniščik, Totally geodesic submanifolds of symmetric spaces, Geometric
methods in problems of algebra and analysis. Vol. 2, Yaroslav. Gos. Univ., Yaroslavl'1980 …

We survey applications of holonomic methods to the study of submanifold geometry,
showing the consequences of some sort of extrinsic version of de Rham decomposition and …