Lumiste Semiparallel Submanifolds in Space Forms

1. Auflage 2009
ISBN: 978-0-387-49913-0
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 306 Seiten, Web PDF

Reihe: Mathematics and Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Lumiste, Ülo

Inhaltsverzeichnis

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.

Über Autor(innen)

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.