Overview
- Provides a comprehensive introduction to submanifold theory
- Engages the reader throughout with many examples and exercises
- Reaches the frontier of knowledge in the subject?
Part of the book series: Universitext (UTX)
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Table of contents (17 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“I can recommend this book to anyone interested in submanifold theory: from students with a background in basic Riemannian geometry to experienced researchers in the field.” (Joeri Van der Veken, Mathematical Reviews, January, 2021)
Authors and Affiliations
About the authors
Marcos Dajczer is a researcher at the Instituto Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. His main field of research is Submanifold Theory and is the author of around 130 articles. He is a fellow of the J. S. Guggenheim Foundation as well as a member of the Brazilian Academy of Sciences (ABC) and The World Academy of Sciences (TWAS). His other interests include natural sciences and politics.
Ruy Tojeiro is currently professor at the University of São Paulo at São Carlos (Brazil), and has been professor at the Federal University of São Carlos until 2018. He has authored over 50 research articles on Submanifold Theory. Besides mathematics, Ruy Tojeiro enjoys playing the baroque recorder.
Bibliographic Information
Book Title: Submanifold Theory
Book Subtitle: Beyond an Introduction
Authors: Marcos Dajczer, Ruy Tojeiro
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4939-9644-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-1-4939-9642-1Published: 03 August 2019
eBook ISBN: 978-1-4939-9644-5Published: 02 August 2019
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XX, 628
Number of Illustrations: 8 b/w illustrations
Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Differential Geometry, General Algebraic Systems