Introduction
This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms. One main theme is the isometric and conformal deformation problem for submanifolds of arbitrary dimension and codimension. Several relevant classes of submanifolds are also discussed, including constant curvature submanifolds, submanifolds of nonpositive extrinsic curvature, conformally flat submanifolds and real Kaehler submanifolds. This is the first textbook to treat a substantial proportion of the material presented here. The first chapters are suitable for an introductory course on Submanifold theory for students with a basic background on Riemannian geometry. The remaining chapters could be used in a more advanced course by students aiming at initiating research on the subject, and are also intended to serve as a reference for specialists in the field.
Keywords
conformal immersion isometric immersion rigidity and deformation submanifold Submanifold theory conformal immersions isometric immersions of warped products genuine deformations infinitesimal bendings real Kaehler submanifolds
Author(s): Marcos Dajczer,Ruy Tojeiro
Series: Universitext
Publisher: Springer International Publishing
Year: 2019
Language: English
Pages: 637
Front Matter ....Pages i-xx
The Basic Equations of a Submanifold (Marcos Dajczer, Ruy Tojeiro)....Pages 1-61
Reduction of Codimension (Marcos Dajczer, Ruy Tojeiro)....Pages 63-84
Minimal Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 85-108
Local Rigidity of Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 109-137
Constant Curvature Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 139-168
Submanifolds with Nonpositive Extrinsic Curvature (Marcos Dajczer, Ruy Tojeiro)....Pages 169-183
Submanifolds with Relative Nullity (Marcos Dajczer, Ruy Tojeiro)....Pages 185-220
Isometric Immersions of Riemannian Products (Marcos Dajczer, Ruy Tojeiro)....Pages 221-251
Conformal Immersions (Marcos Dajczer, Ruy Tojeiro)....Pages 253-307
Isometric Immersions of Warped Products (Marcos Dajczer, Ruy Tojeiro)....Pages 309-356
The Sbrana–Cartan Hypersurfaces (Marcos Dajczer, Ruy Tojeiro)....Pages 357-385
Genuine Deformations (Marcos Dajczer, Ruy Tojeiro)....Pages 387-452
Deformations of Complete Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 453-475
Infinitesimal Bendings (Marcos Dajczer, Ruy Tojeiro)....Pages 477-499
Real Kaehler Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 501-540
Conformally Flat Submanifolds (Marcos Dajczer, Ruy Tojeiro)....Pages 541-567
Conformally Deformable Hypersurfaces (Marcos Dajczer, Ruy Tojeiro)....Pages 569-598
Back Matter ....Pages 599-628
