| Riemannian Geometry: Theory & Applications 1992, Corr. 14t Edition Contributor(s): Do Carmo, Manfredo P. (Author), Flaherty, Francis (Translator) |
|
 |
ISBN: 0817634908 ISBN-13: 9780817634902 Publisher: Birkhauser OUR PRICE: $47.49 Product Type: Hardcover Published: January 1992 Annotation: This text has been adopted at: University of Pennsylvania, Philadelphia University of Connecticut, Storrs Duke University, Durham, NC California Institute of Technology, Pasadena University of Washington, Seattle Swarthmore College, Swarthmore, PA University of Chicago, IL University of Michigan, Ann Arbor "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." Revue Romaine de Mathematiques Pures et Appliquees "This main-stream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." Monatshefte F. Mathematik "This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." Publicationes Mathematicae Contents: Differential Manifolds * Riemannian Metrics * Affine Connections; Riemannian Connections * Geodesics; Convex Neighborhoods * Curvature * Jacobi Fields * Isometric Immersions * Complete Manifolds; Hopf-Rinow and Hadamard Theorems * Spaces of Constant Curvature * Variations of Energy * The Rauch Comparison Theorem * The Morse Index Theorem * The Fundamental Group of Manifolds of Negative Curvature * The Sphere Theorem * Index Series: Mathematics: Theory and Applications |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Analytic - Science | Physics - Mathematical & Computational - Mathematics | Geometry - Differential |
| Dewey: 516.373 |
| LCCN: 91037377 |
| Series: Mathematics: Theory & Applications |
| Physical Information: 0.7" H x 7.4" W x 8.7" (1.20 lbs) 300 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text. A significant feature of the book is its powerful and revealing structure, beginning simply with the definition of a differentiable manifold and ending with one of the most important results in Riemannian geometry, a proof of the Sphere Theorem. The text abounds with basic definitions and theorems, examples, applications, and numerous exercises to test the student's understanding and extend knowledge and insight into the subject. Instructors and students alike will find the work to be a significant contribution to this highly applicable and stimulating subject. |