Semiparallel submanifolds in space forms

Ülo Lumiste (auth.)9780387499130, 9780387499116, 0387499113

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.

Table of contents :
Front Matter….Pages 1-6
Introduction….Pages 1-6
Preliminaries….Pages 1-15
Submanifolds in Space Forms….Pages 1-10
Parallel Submanifolds….Pages 1-17
Semiparallel Submanifolds….Pages 1-22
Normally Flat Semiparallel Submanifolds….Pages 1-23
Semiparallel Surfaces….Pages 1-37
Semiparallel Three-Dimensional Submanifolds….Pages 1-22
Decomposition Theorems….Pages 1-17
Umbilic-Likeness of Main Symmetric Orbits….Pages 1-44
Geometric Descriptions in General….Pages 1-18
Isometric Semiparallel Immersions of Riemannian Manifolds of Conullity Two….Pages 1-11
Some Generalizations….Pages 1-37
Back Matter….Pages 1-20