61,85 €*
Versandkostenfrei per Post / DHL
Lieferzeit 1-2 Wochen
Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré¿Hopf and Chern¿Gauss¿Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material.
The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré¿Hopf and Chern¿Gauss¿Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material.
The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
Kai Köhler is Professor of Mathematics at the Heinrich Heine University of Düsseldorf. His research area is Geometry, with an emphasis on Global Analysis and Arithmetic Algebraic Geometry.
1 Manifolds.- 2 Vector Bundles and Tensors.- 3 Riemannian Manifolds.- 4 The Poincaré-Hopf Theorem and the Chern-Gauß-Bonnet Theorem.- 5 Geodesics.- 6 Homogeneous Spaces.- 7 Symmetric Spaces.- 8 General Relativity.- A Solutions to Selected Exercises.
| Erscheinungsjahr: | 2024 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
x
292 S. |
| ISBN-13: | 9783662697207 |
| ISBN-10: | 3662697203 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Köhler, Kai |
| Hersteller: |
Springer Berlin
Springer Berlin Heidelberg |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 16 mm |
| Von/Mit: | Kai Köhler |
| Erscheinungsdatum: | 30.10.2024 |
| Gewicht: | 0,519 kg |
Kai Köhler is Professor of Mathematics at the Heinrich Heine University of Düsseldorf. His research area is Geometry, with an emphasis on Global Analysis and Arithmetic Algebraic Geometry.
1 Manifolds.- 2 Vector Bundles and Tensors.- 3 Riemannian Manifolds.- 4 The Poincaré-Hopf Theorem and the Chern-Gauß-Bonnet Theorem.- 5 Geodesics.- 6 Homogeneous Spaces.- 7 Symmetric Spaces.- 8 General Relativity.- A Solutions to Selected Exercises.
| Erscheinungsjahr: | 2024 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
x
292 S. |
| ISBN-13: | 9783662697207 |
| ISBN-10: | 3662697203 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Köhler, Kai |
| Hersteller: |
Springer Berlin
Springer Berlin Heidelberg |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 16 mm |
| Von/Mit: | Kai Köhler |
| Erscheinungsdatum: | 30.10.2024 |
| Gewicht: | 0,519 kg |
Ähnliche Produkte
Lieferzeit 1-2 Werktage
Lieferzeit 4-7 Werktage
Aktuell nicht verfügbar
Lieferzeit 1-2 Wochen
Lieferzeit 1-2 Wochen
Lieferzeit 2-4 Werktage
Lieferzeit 1-2 Wochen
Lieferzeit 4-7 Werktage