Semiparallel Submanifolds in Space Forms

This book offers the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, detailing symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. The book then introduces semiparallel submanifolds and gives some characterizations for their class and several subclasses. Coverage next discusses the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. Presenting both background material and the most recent developments in semiparallel submanifolds, this book will appeal to both researchers and graduate students.