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 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 …

We introduce a geometric invariant that we call the index of symmetry, which measures how
far is a Riemannian manifold from being a symmetric space. We compute, in a geometric …

We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie
algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal …

We develop a general structure theory for compact homogeneous Riemannian manifolds in
relation to the coindex of symmetry. We will then use these results to classify irreducible …

We discuss the rigidity (or lack thereof) imposed by different notions of having an abundance
of zero curvature planes on a complete Riemannian $3 $-manifold. We prove a rank rigidity …

Berwald metrics are particular Finsler metrics which still have linear Berwald connections.
Their complete classification is established in an earlier work,[Sz1], of this author. The main …

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 …

We prove the polarity of the normal holonomy of riemannian submanifolds of lorentzian
space. Using this result we prove that, essentially, there is no submanifold of hyperbolic …

If M is a submanifold of a space form, the nullity distribution N of its second fundamental form
is (when defined) the common kernel of its shape operators. In this paper we will give a local …