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Series : Springer Monographs in Mathematics

Semiparallel Submanifolds in Space Forms

Semiparallel Submanifolds in Space Forms
Author
Lumiste, ulo 
Publisher
Springer-Verlag 
Publication Date
Oct, 2008 
ISBN
0387499113 or 9780387499116
HARDCOVER 
306 Pages
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¥ 17,110 (tax included)

Description

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. Lumiste 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.

Contents

Introduction

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

Bibliography

Index.

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