Riemannian Geometry

• Main Author: Petersen, Peter (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Edition: 3rd ed. 2016.
• Series: Graduate Texts in Mathematics, 171
• Subjects: Mathematics.; Differential geometry.; Differential Geometry.

Intended for a one year course, this text serves as a single source, introducing readers 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 comb...

Table of Contents:

• Preface
• 1. Riemannian Metrics.-2. Derivatives
• 3. Curvature
• 4. Examples
• 5. Geodesics and Distance
• 6. Sectional Curvature Comparison I.- 7. Ricci Curvature Comparison.- 8. Killing Fields
• 9. The Bochner Technique
• 10. Symmetric Spaces and Holonomy
• 11. Convergence
• 12. Sectional Curvature Comparison II
• Bibliography
• Index.