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

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- 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