Semiparallel Submanifolds in Space Forms (Hardback)Ulo Lumiste (author)
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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.
Publisher: Springer-Verlag New York Inc.
Number of pages: 306
Weight: 637 g
Dimensions: 235 x 155 x 19 mm
Edition: 2009 ed.
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)