Semiparallel Submanifolds in Space Forms Softcover reprint of hardcover 1st ed. 2009 Edition

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 monograph … take the reader from the fundamentals of the theory to the latest research. … The book can be effectively used as a textbook for a graduate level course or a research seminar on the topic of parallel and semiparallel submanifolds … .” (Ivko Dimitric, Mathematical Reviews, Issue 2010 h)

This book offers a comprehensive survey to date of the theory of semiparallel submanifolds. Introduced in 1985, semiparallel submanifolds have emerged as an important area of research within differential geometry and topology.

The author begins with the necessary background on symmetric and semisymmetric Riemannian manifolds, smooth manifolds in space forms, and parallel submanifolds. Semiparallel submanifolds are introduced in Chapter 4, where characterizations of their class and several subclasses are given. In later chapters Lumiste introduces the concept of main symmetric orbit and presents all known results concerning umbilic-like main symmetric orbits. Generalizations, such as k-semiparallel submanifolds and Ric-semiparallel hypersurfaces, are also studied.

Semiparallel Submanifolds in Space Forms will appeal to both researchers and graduate students.