Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.

• 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.

“This is a very advanced textbook on metric and algebraic proofs of critical theorems in the field of metric spaces involving manifolds and other 3D structures. … First, definitions, theorems, proofs, and exercises abound throughout every section of this 500 page mathematics book. The history of development in the area is comprehensive. … The experts will find this a useful research tool. … I recommend this book for researchers having a strong background to begin with.” (Joseph J. Grenier, Amazon.com, June, 2016)

Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.

• 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.

“This is a very advanced textbook on metric and algebraic proofs of critical theorems in the field of metric spaces involving manifolds and other 3D structures. … First, definitions, theorems, proofs, and exercises abound throughout every section of this 500 page mathematics book. The history of development in the area is comprehensive. … The experts will find this a useful research tool. … I recommend this book for researchers having a strong background to begin with.” (Joseph J. Grenier, Amazon.com, June, 2016)

Peter Petersen is a Professor of Mathematics at UCLA. His current research is on various aspects of Riemannian geometry. Professor Petersen has authored two important textbooks for Springer: Riemannian Geometry in the GTM series and Linear Algebra in the UTM series.

• 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.

“This is a very advanced textbook on metric and algebraic proofs of critical theorems in the field of metric spaces involving manifolds and other 3D structures. … First, definitions, theorems, proofs, and exercises abound throughout every section of this 500 page mathematics book. The history of development in the area is comprehensive. … The experts will find this a useful research tool. … I recommend this book for researchers having a strong background to begin with.” (Joseph J. Grenier, Amazon.com, June, 2016)