skip to content
Introduction to smooth manifolds Preview this item
ClosePreview this item
Checking...

Introduction to smooth manifolds

Author: John M Lee
Publisher: New York : Springer, ©2003.
Series: Graduate texts in mathematics, 218.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Lee, John M., 1950-
Introduction to smooth manifolds.
New York : Springer, ©2003
(DLC) 2002070454
(OCoLC)49681196
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: John M Lee
ISBN: 9780387217529 0387217525 0387954953 9780387954950 1280189789 9781280189784 0387954481 9780387954486
OCLC Number: 666929817
Description: 1 online resource (xvii, 628 pages) : illustrations
Contents: Preface --
Smooth Manifolds --
Smooth Maps --
Tangent Vectors --
Vector Fields --
Vector Bundles --
The Cotangent Bundle --
Submersions, Immersions, and Embeddings --
Submanifolds --
Embedding and Approximation Theorems --
Lie Group Actions --
Tensors --
Differential Forms --
Orientations --
Integration on Manifolds --
De Rham Cohomology --
The De Rham Theorem --
Integral Curves and Flows --
Lie Derivatives --
Integral Manifolds and Foliations --
Lie Groups and Their Lie Algebras --
Appendix: Review of Prerequisites --
References --
Index.
Series Title: Graduate texts in mathematics, 218.
Responsibility: John M. Lee.

Abstract:

A sequel to "Introduction to Topological Manifolds". This title includes explanations, diagrams and exemplary motivation, short preliminary sections before each section explaining what is ahead and  Read more...

Reviews

Editorial reviews

Publisher Synopsis

From the reviews: "This book offers a concise, clear, and detailed introduction to analysis on manifolds and elementary differential geometry. ... Some of the prerequisites are reviewed in an Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


\n\n

Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/666929817<\/a>> # Introduction to smooth manifolds<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Book<\/a>, schema:MediaObject<\/a>, schema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"666929817<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> ; # New York<\/span>\n\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/nyu<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/variedades_diferenciaveis<\/a>> ; # Variedades diferenci\u00E1veis<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/geometry<\/a>> ; # Geometry<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/dewey.info\/class\/514.3\/e21\/<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/physical_sciences_&_mathematics<\/a>> ; # Physical Sciences & Mathematics<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_flache<\/a>> ; # Glatte Fl\u00E4che<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/mathematics<\/a>> ; # Mathematics<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/manifolds<\/a>> ; # Manifolds<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_mannigfaltigkeit<\/a>> ; # Glatte Mannigfaltigkeit<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/varietes_mathematiques<\/a>> ; # Vari\u00E9t\u00E9s (Math\u00E9matiques)<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/id.worldcat.org\/fast\/1007726<\/a>> ; # Manifolds (Mathematics)<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_kurve<\/a>> ; # Glatte Kurve<\/span>\n\u00A0\u00A0\u00A0\nschema:bookFormat<\/a> schema:EBook<\/a> ;\u00A0\u00A0\u00A0\nschema:copyrightYear<\/a> \"2003<\/span>\" ;\u00A0\u00A0\u00A0\nschema:creator<\/a> <http:\/\/viaf.org\/viaf\/19832377<\/a>> ; # John M. Lee<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2003<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Preface -- Smooth Manifolds -- Smooth Maps -- Tangent Vectors -- Vector Fields -- Vector Bundles -- The Cotangent Bundle -- Submersions, Immersions, and Embeddings -- Submanifolds -- Embedding and Approximation Theorems -- Lie Group Actions -- Tensors -- Differential Forms -- Orientations -- Integration on Manifolds -- De Rham Cohomology -- The De Rham Theorem -- Integral Curves and Flows -- Lie Derivatives -- Integral Manifolds and Foliations -- Lie Groups and Their Lie Algebras -- Appendix: Review of Prerequisites -- References -- Index.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author\'s last book, Introduction to Topological Manifolds(2000). While the subject is often called \"differential geometry,\" in this book the author has decided to avoid use of this term because it applies more specifically to the study of smooth manifolds endowed with some extra structure, such as a Riemannian metric, a symplectic structure, a Lie group structure, or a foliation, and of the properties that are invariant under maps that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/4918464809<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Electronic books<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"en<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isPartOf<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Series\/graduate_texts_in_mathematics<\/a>> ; # Graduate texts in mathematics ;<\/span>\n\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/www.worldcat.org\/oclc\/49681196<\/a>> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Introduction to smooth manifolds<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"666929817<\/span>\" ;\u00A0\u00A0\u00A0\nschema:publication<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/666929817#PublicationEvent\/new_york_springer_2003<\/a>> ;\u00A0\u00A0\u00A0\nschema:publisher<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Agent\/springer<\/a>> ; # Springer<\/span>\n\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/doi.org\/10.1007\/978-0-387-21752-9<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.vlebooks.com\/vleweb\/product\/openreader?id=none&isbn=9780387217529<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/dx.doi.org\/10.1007\/978-0-387-21752-9<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.myilibrary.com?id=18978&ref=toc<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/0-link-springer-com.pugwash.lib.warwick.ac.uk\/10.1007\/978-0-387-21752-9<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.myilibrary.com?id=18978<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780387954950<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/dx.doi.org\/10.1007\/978-0-387-21752-9<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780387217529<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9781280189784<\/a>> ;\u00A0\u00A0\u00A0\nschema:workExample<\/a> <http:\/\/worldcat.org\/isbn\/9780387954486<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/666929817<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Related Entities<\/h3>\n
<http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> # New York<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"New York<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/dewey.info\/class\/514.3\/e21\/<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/dx.doi.org\/10.1007\/978-0-387-21752-9<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:IndividualProduct<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Agent\/springer<\/a>> # Springer<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:Agent<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Springer<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Series\/graduate_texts_in_mathematics<\/a>> # Graduate texts in mathematics ;<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nbgn:PublicationSeries<\/a> ;\u00A0\u00A0\u00A0\nschema:hasPart<\/a> <http:\/\/www.worldcat.org\/oclc\/666929817<\/a>> ; # Introduction to smooth manifolds<\/span>\n\u00A0\u00A0\u00A0\nschema:name<\/a> \"Graduate texts in mathematics ;<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/geometry<\/a>> # Geometry<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Geometry<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_flache<\/a>> # Glatte Fl\u00E4che<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Glatte Fl\u00E4che<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_kurve<\/a>> # Glatte Kurve<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Glatte Kurve<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/glatte_mannigfaltigkeit<\/a>> # Glatte Mannigfaltigkeit<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Glatte Mannigfaltigkeit<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/manifolds<\/a>> # Manifolds<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Manifolds<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/mathematics<\/a>> # Mathematics<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Mathematics<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/physical_sciences_&_mathematics<\/a>> # Physical Sciences & Mathematics<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Physical Sciences & Mathematics<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/variedades_diferenciaveis<\/a>> # Variedades diferenci\u00E1veis<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Variedades diferenci\u00E1veis<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Topic\/varietes_mathematiques<\/a>> # Vari\u00E9t\u00E9s (Math\u00E9matiques)<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Vari\u00E9t\u00E9s (Math\u00E9matiques)<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/nyu<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"nyu<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.worldcat.org\/fast\/1007726<\/a>> # Manifolds (Mathematics)<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Manifolds (Mathematics)<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/viaf.org\/viaf\/19832377<\/a>> # John M. Lee<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1950<\/span>\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Lee<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"John M.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"John M. Lee<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9780387217529<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0387217525<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780387217529<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9780387954486<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0387954481<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780387954486<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9780387954950<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"0387954953<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9780387954950<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/worldcat.org\/isbn\/9781280189784<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:ProductModel<\/a> ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"1280189789<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isbn<\/a> \"9781280189784<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/oclc\/49681196<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:CreativeWork<\/a> ;\u00A0\u00A0\u00A0\nrdfs:label<\/a> \"Introduction to smooth manifolds.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Print version:<\/span>\" ;\u00A0\u00A0\u00A0\nschema:isSimilarTo<\/a> <http:\/\/www.worldcat.org\/oclc\/666929817<\/a>> ; # Introduction to smooth manifolds<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/666929817<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/666929817<\/a>> ; # Introduction to smooth manifolds<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2020-06-23<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/666929817#PublicationEvent\/new_york_springer_2003<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:PublicationEvent<\/a> ;\u00A0\u00A0\u00A0\nschema:location<\/a> <http:\/\/dbpedia.org\/resource\/New_York_City<\/a>> ; # New York<\/span>\n\u00A0\u00A0\u00A0\nschema:organizer<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4918464809#Agent\/springer<\/a>> ; # Springer<\/span>\n\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n