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Einfhrung in die Geometrie und Topologie by Werner Ballmann (German) Paperback B
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Item specifics
- Condition
- ISBN-13
- 9783034809856
- Book Title
- Einfhrung in die Geometrie und Topologie
- ISBN
- 9783034809856
- Subject Area
- Mathematics
- Publication Name
- Einführung in Die Geometrie Und Topologie
- Publisher
- Springer Basel A&G
- Item Length
- 9.4 in
- Subject
- Geometry / Differential, Topology, Mathematical Analysis
- Publication Year
- 2018
- Series
- Mathematik Kompakt Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- German
- Item Weight
- 16 Oz
- Item Width
- 6.6 in
- Number of Pages
- Xii, 163 Pages
About this product
Product Information
Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Nach einer Einführung in grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie wird der Jordansche Kurvensatz für Polygonzüge bewiesen und damit eine erste Idee davon vermittelt, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. In der zweiten Auflage habe ich eine Reihe von Textstellen leicht überarbeitet und einige Fehler berichtigt.
Product Identifiers
Publisher
Springer Basel A&G
ISBN-10
3034809859
ISBN-13
9783034809856
eBay Product ID (ePID)
18038573821
Product Key Features
Number of Pages
Xii, 163 Pages
Language
German
Publication Name
Einführung in Die Geometrie Und Topologie
Publication Year
2018
Subject
Geometry / Differential, Topology, Mathematical Analysis
Type
Textbook
Subject Area
Mathematics
Series
Mathematik Kompakt Ser.
Format
Trade Paperback
Dimensions
Item Weight
16 Oz
Item Length
9.4 in
Item Width
6.6 in
Additional Product Features
Edition Number
2
Number of Volumes
1 Vol.
Illustrated
Yes
Lc Classification Number
Qa613-613.8
Table of Content
I. Erste Schritte in die Topologie.- II. Mannigfaltigkeiten.- III. Differentialformen und Kohomologie.- IV. Geometrie von Untermannigfaltigkeiten.- A. Alternierende Multilinearformen.- B. Kokettenkomplexe.- Literaturverzeichnis.- Index.
Copyright Date
2018
Item description from the seller
Seller assumes all responsibility for this listing.
eBay item number:364699197590
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