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Important revisions to the third edition include:
a substantial addition of unique and enriching exercises scattered throughout the text;
inclusion of an increased number of coordinate calculations of connection and curvature;
addition of general formulas for curvature on Lie Groups and submersions;
integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger;
incorporation of several recent results about manifolds with positive curvature;
presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds.
From reviews of the first edition:
"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."
¿Bernd Wegner, ZbMATH
Important revisions to the third edition include:
a substantial addition of unique and enriching exercises scattered throughout the text;
inclusion of an increased number of coordinate calculations of connection and curvature;
addition of general formulas for curvature on Lie Groups and submersions;
integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger;
incorporation of several recent results about manifolds with positive curvature;
presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds.
From reviews of the first edition:
"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."
¿Bernd Wegner, ZbMATH
Includes a substantial addition of unique and enriching exercises
Exists as one of the few Works to combine both the geometric parts of Riemannian geometry and analytic aspects of the theory
Presents a new approach to the Bochner technique for tensors that considerably simplifies the material
Includes supplementary material: [...]
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 520 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xviii
499 S. 49 s/w Illustr. 1 farbige Illustr. 499 p. 50 illus. 1 illus. in color. |
| ISBN-13: | 9783319266527 |
| ISBN-10: | 3319266527 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-26652-7 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Petersen, Peter |
| Auflage: | 3rd ed. 2016 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 32 mm |
| Von/Mit: | Peter Petersen |
| Erscheinungsdatum: | 31.03.2016 |
| Gewicht: | 1,034 kg |
Includes a substantial addition of unique and enriching exercises
Exists as one of the few Works to combine both the geometric parts of Riemannian geometry and analytic aspects of the theory
Presents a new approach to the Bochner technique for tensors that considerably simplifies the material
Includes supplementary material: [...]
| Erscheinungsjahr: | 2016 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 520 |
| Reihe: | Graduate Texts in Mathematics |
| Inhalt: |
xviii
499 S. 49 s/w Illustr. 1 farbige Illustr. 499 p. 50 illus. 1 illus. in color. |
| ISBN-13: | 9783319266527 |
| ISBN-10: | 3319266527 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-26652-7 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: | Petersen, Peter |
| Auflage: | 3rd ed. 2016 |
| Hersteller: |
Springer International Publishing
Graduate Texts in Mathematics |
| Maße: | 241 x 160 x 32 mm |
| Von/Mit: | Peter Petersen |
| Erscheinungsdatum: | 31.03.2016 |
| Gewicht: | 1,034 kg |
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