Submanifold theory has emerged as a natural development of the classical study of curves
and surfaces in Euclidean three space with the methods of differential calculus. In the last …

In this chapter, we give Lie's construction of the space of spheres and define the important
notions of oriented contact and parabolic pencils of spheres. This leads ultimately to a …

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 …

Hermitian symmetric spaces are an important class of manifolds that can be studied with
methods from Kähler geometry and Lie theory. This work gives an introduction to Hermitian …

We classify the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane
Grassmannians SU2, m/S (U2⋅ Um), m⩾ 2. Each can be described as a tube over a totally …

First, we introduce the notion of shape operator of Codazzi type for real hypersurfaces in the
complex quadric Qm= SOm+ 2/SOmSO2. Next, we give a complete proof of non-existence of …

In this paper, we classify the hypersurfaces of S 2× S 2 with constant sectional curvature. We
prove that the constant sectional curvature can only be 1 2. We show that any such …

We classify real hypersurfaces with isometric Reeb flow in the complex quadrics Qm= SOm+
2/SOmSO2, m≥ 3. We show that m is even, say m= 2k, and any such hypersurface is an …

A contact hypersurface in a Kähler manifold is a real hypersurface for which the induced
almost contact metric structure determines a contact structure. We carry out a systematic …

In our previous work, we studied isoparametric functions on Riemannian manifolds,
especially on exotic spheres. One result there says that, in the family of isoparametric …