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Submanifold Theory

Beyond an Introduction

  • Marcos Dajczer
  • Ruy Tojeiro
Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Marcos Dajczer, Ruy Tojeiro
    Pages 1-61
  3. Marcos Dajczer, Ruy Tojeiro
    Pages 63-84
  4. Marcos Dajczer, Ruy Tojeiro
    Pages 85-108
  5. Marcos Dajczer, Ruy Tojeiro
    Pages 109-137
  6. Marcos Dajczer, Ruy Tojeiro
    Pages 139-168
  7. Marcos Dajczer, Ruy Tojeiro
    Pages 169-183
  8. Marcos Dajczer, Ruy Tojeiro
    Pages 185-220
  9. Marcos Dajczer, Ruy Tojeiro
    Pages 221-251
  10. Marcos Dajczer, Ruy Tojeiro
    Pages 253-307
  11. Marcos Dajczer, Ruy Tojeiro
    Pages 309-356
  12. Marcos Dajczer, Ruy Tojeiro
    Pages 357-385
  13. Marcos Dajczer, Ruy Tojeiro
    Pages 387-452
  14. Marcos Dajczer, Ruy Tojeiro
    Pages 453-475
  15. Marcos Dajczer, Ruy Tojeiro
    Pages 477-499
  16. Marcos Dajczer, Ruy Tojeiro
    Pages 501-540
  17. Marcos Dajczer, Ruy Tojeiro
    Pages 541-567
  18. Marcos Dajczer, Ruy Tojeiro
    Pages 569-598
  19. Back Matter
    Pages 599-628

About this book

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

Authors and affiliations

  • Marcos Dajczer
    • 1
  • Ruy Tojeiro
    • 2
  1. 1.IMPARio de JaneiroBrazil
  2. 2.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-9644-5
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2019
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-9642-1
  • Online ISBN 978-1-4939-9644-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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