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 …

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 …

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie
group $\mathsf {G} $ with compact, smooth orbit space, we show that the nilradical $\mathsf …

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

A singular foliation on a complete riemannian manifold is said to be riemannian if every
geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it …

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 foliation F on a Riemannian manifold M is hyperpolar if it admits a flat section, that is, a
connected closed flat submanifold of M that intersects each leaf of F orthogonally. In this …

These are the notes for a series of lectures at the Institute of Geometry and Topology of the
University of Stuttgart, Germany, in July 13-15, 2022. We assume basic knowledge of …

We investigate orthogonal representations of compact Lie groups from the point of view of
their quotient spaces, considered as metric spaces. We study metric spaces which are …

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 …