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 …

The main purpose of this book is to give an exposition of recent results (obtained with the
essential participation of the authors) on geodesic orbit Riemannian manifolds and their …

We present a new method for classifying naturally reductive homogeneous spaces–ie
homogeneous Riemannian manifolds admitting a metric connection with skew torsion that …

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a
connection∇ with skew-symmetric torsion. We derive the Einstein equation from a …

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 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 …

A Riemann–Cartan manifold is a Riemannian manifold endowed with an affine connection
which is compatible with the metric tensor. This affine connection is not necessarily torsion …

For a compact connected Lie group $ G $ we study the class of bi-invariant affine
connections whose geodesics through $ e\in G $ are the 1-parameter subgroups. We show …

The full classification of Riemannian $3 $-symmetric spaces is presented. Up to Riemannian
products the main building blocks consist in (possibly symmetric) spaces with semisimple …

In the absence of a de Rham decomposition theorem for geometries with torsion, we
develop and unify ways to view a geometry with parallel skew torsion as the total space of a …