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Beschreibung
Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research.
Important additions to this new edition include:
- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise
- An increased number of coordinate calculations of connection and curvature
- General fomulas for curvature on Lie Groups and submersions
- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger
- Several recent results about manifolds with positive curvature
Important additions to this new edition include:
- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise
- An increased number of coordinate calculations of connection and curvature
- General fomulas for curvature on Lie Groups and submersions
- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger
- Several recent results about manifolds with positive curvature
Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research.
Important additions to this new edition include:
- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise
- An increased number of coordinate calculations of connection and curvature
- General fomulas for curvature on Lie Groups and submersions
- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger
- Several recent results about manifolds with positive curvature
Important additions to this new edition include:
- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise
- An increased number of coordinate calculations of connection and curvature
- General fomulas for curvature on Lie Groups and submersions
- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger
- Several recent results about manifolds with positive curvature
Zusammenfassung
Designed for a one year introductory course, this volume introduces students to the important techniques and theorems of Riemannian geometry, while presenting sufficient background on advanced topics to appeal to students who wish to specialize in the discipline. The text combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and presents the most up-to-date research. The updated second edition includes such new material as: A completely new coordinate-free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgotten proof by Berger; several recent results regarding manifolds with positive curvature.
Inhaltsverzeichnis
Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.
Details
| Erscheinungsjahr: | 2010 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xv
405 S. |
| ISBN-13: | 9781441921239 |
| ISBN-10: | 1441921230 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Petersen, Peter |
| Auflage: | Softcover reprint of hardcover 2nd edition 2006 |
| Hersteller: |
Springer US
Springer New York |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 23 mm |
| Von/Mit: | Peter Petersen |
| Erscheinungsdatum: | 23.11.2010 |
| Gewicht: | 0,639 kg |
Zusammenfassung
Designed for a one year introductory course, this volume introduces students to the important techniques and theorems of Riemannian geometry, while presenting sufficient background on advanced topics to appeal to students who wish to specialize in the discipline. The text combines both the geometric parts of Riemannian geometry and the analytic aspects of the theory, and presents the most up-to-date research. The updated second edition includes such new material as: A completely new coordinate-free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgotten proof by Berger; several recent results regarding manifolds with positive curvature.
Inhaltsverzeichnis
Riemannian Metrics.- Curvature.- Examples.- Hypersurfaces.- Geodesics and Distance.- Sectional Curvature Comparison I.- The Bochner Technique.- Symmetric Spaces and Holonomy.- Ricci Curvature Comparison.- Convergence.- Sectional Curvature Comparison II.
Details
| Erscheinungsjahr: | 2010 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: |
xv
405 S. |
| ISBN-13: | 9781441921239 |
| ISBN-10: | 1441921230 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Petersen, Peter |
| Auflage: | Softcover reprint of hardcover 2nd edition 2006 |
| Hersteller: |
Springer US
Springer New York |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 23 mm |
| Von/Mit: | Peter Petersen |
| Erscheinungsdatum: | 23.11.2010 |
| Gewicht: | 0,639 kg |
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