The purpose of this book is to provide a thorough, up-to-date treatment of the differential
geometry of hypersurfaces in real, complex, and quaternionic space forms. Special …

This book is intended for advanced undergraduates, graduate students, and young
researchers in geometry. It was written with two main goals in mind. First, we give a gentle …

Given a real inner product space V and a group G of linear isometries, max filtering offers a
rich class of G-invariant maps. In this paper, we identify nearly sharp conditions under which …

An equidistant decomposition F of a metric space X is a decomposition of X into a collection
of pairwise equidistant closed subsets Li; i 2 I, called the leaves of the decomposition. The …

We prove a slice theorem around closed leaves in a singular Riemannian foliation, and we
use it to study the $ C^\infty $-algebra of smooth basic functions, generalizing to the …

We characterize Riemannian orbifolds and their coverings in terms of metric geometry. In
particular, we show that the metric double of a Riemannian orbifold along the closure of its …

Singular Riemannian Foliations and Isoparametric Submanifolds Page 1 Singular Riemannian
Foliations and Isoparametric Submanifolds Gudlaugur Thorbergsson Abstract. We will explain …

We prove that an isometric action of a Lie group on a Riemannian manifold admits a
resolution preserving the transverse geometry if and only if the action is infinitesimally polar …

A singular foliation is called a singular Riemannian foliation (SRF) if every geodesic that is
perpendicular to one leaf is perpendicular to every leaf it meets. A typical example is the …

A group action is called polar if there exists an immersed submanifold (a section) which
intersects all orbits orthogonally. We show how to construct a manifold admitting a polar …