Semiparallel Submanifolds in Space Forms [Paperback]

Quite simply, 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 as well as several subclasses. The coverage moves on to discuss the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. With more than 40 published papers under his belt on the subject, Lumiste provides readers with the most authoritative treatment.

Quite simply, this book is the most comprehensive survey to date of the theory of semiparallel submanifolds. It begins with the necessary background material, then introduces semiparallel submanifolds and gives some characterizations for their class as well as several subclasses.

Preliminaries.- Submanifolds in Space Forms.- Parallel Submanifolds.- Semiparallel Submanifolds.- Normally Flat Semiparallel Submanifolds.- Semiparallel Surfaces.- Semiparallel Three-Dimensional Submanifolds.- Decomposition Theorems.- Umbilic-Likeness of Main Symmetric Orbits.- Geometric Descriptions in General.- Isometric Semiparallel Immersions of Riemannian Manifolds of Conullity Two.- Some Generalizations.

From the reviews:

This is a nice book concerning submanifolds of space forms with semiparallel second fundamental form & . the present book is strongly recommended to both beginner and advance researchers in the geometry of submanifolds. (Constantin Calin, Zentralblatt MATH, Vol. 1156, 2009)

This monograph represents a comprehensive survey and a fine contribution of the author on the topic of semiparallel submanifolds & . The book is intended for graduate students and researchers working in the area of Riemannian submanifolds. The monlãì