Ülo Lumiste

Semiparallel Submanifolds in Space Forms (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 306
• Erscheinungstermin: 2. März 2009
• Englisch
• ISBN-13: 9780387499130
• Artikelnr.: 37286788

Autorenporträt

Ülo Lumiste is considered an expert in the application of Cartan's exterior calculus. He has been noted for his extensive contributions to the area of semiparallel submanifolds.

Inhaltsangabe

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.

Rezensionen

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)