Submanifolds and Holonomy

Praise for the First Edition:"This book is carefully written; it contains some new proofs and open problems, many exercises and references, and an appendix for basic materials, and so it would be very useful not only for researchers but also graduate students in geometry."
—Mathematical Reviews, Issue 2004e

"This book is a valuable addition to the literature on the geometry of submanifolds. It gives a comprehensive presentation of several recent developments in the theory, including submanifolds with parallel second fundamental form, isoparametric submanifolds and their Coxeter groups, and the normal holonomy theorem. Of particular importance are the isotropy representations of semisimple symmetric spaces, which play a unifying role in the text and have several notable characterizations. The book is well organized and carefully written, and it provides an excellent treatment of an important part of modern submanifold theory."
—Thomas E. Cecil, Professor of Mathematics, College of the Holy Cross, Worcester, Massachusetts, USA

"The study of submanifolds of Euclidean space and more generally of spaces of constant curvature has a long history. While usually only surfaces or hypersurfaces are considered, the emphasis of this monograph is on higher co-dimension. Exciting beautiful results have emerged in recent years in this area and are all presented in this volume, many of them for the first time in book form. One of the principal tools of the authors is the holonomy group of the normal bundle of the submanifold and the surprising result of C. Olmos, which parallels Marcel Berger’s classification in the Riemannian case. Great efforts have been made to develop the whole theory from scratch and simplify existing proofs. The book will surely become an indispensable tool for anyone seriously interested in submanifold geometry."
—Professor Ernst Heintze, Institut für Mathematik, Universitaet Augsburg, Germany