By Manfredo P.Do Carmo, M.P. do Carmo, Francis Flaherty
This article has been followed at:
University of Pennsylvania, Philadelphia college of Connecticut, Storrs Duke collage, Durham, NC California Institute of know-how, Pasadena collage of Washington, Seattle Swarthmore collage, Swarthmore, PA college of Chicago, IL collage of Michigan, Ann Arbor
"In the reviewer's opinion, it is a awesome booklet which makes studying a true pleasure."
- Revue Romaine de Mathematiques Pures et Appliquees
"This main-stream presentation of differential geometry serves good for a path on Riemannian geometry, and it truly is complemented through many annotated exercises."
- Monatshefte F. Mathematik
"This is likely one of the most sensible (if even not only the simplest) e-book if you are looking to get an outstanding, gentle and quickly, yet but thorough advent to trendy Riemannian geometry."
- Publicationes Mathematicae
Contents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * whole Manifolds; Hopf-Rinow and Hadamard Theorems * areas of continuous Curvature * diversifications of power * The Rauch comparability Theorem * The Morse Index Theorem * the basic team of Manifolds of damaging Curvature * the field Theorem * Index
Series: arithmetic: thought and purposes