| A.D. Alexandrov: Selected Works Part II: Intrinsic Geometry of Convex Surfaces Contributor(s): Kutateladze, S. S. (Editor) |
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ISBN: 0415298024 ISBN-13: 9780415298025 Publisher: CRC Press OUR PRICE: $228.00 Product Type: Hardcover - Other Formats Published: March 2005 Annotation: A.D. Alexandrov's contribution to the field of intrinsic geometry was original and very influential. This text is a classic that remains unsurpassed in its clarity and scope. It presents his core material, originally published in Russian in 1948, beginning wth an outline of the main concepts and then exploring other topics, such as general propositions on an intrinsic metric; angles and curvature; existence of a convex polyhedron with prescribed metric; curves on convex surfaces; and the role of specific curvature. This text provides Adefinitive source for the development of intrinsic geometry and is indispensable for graduate students who want a better understanding of this subject. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential |
| Dewey: 516.36 |
| LCCN: 2004049387 |
| Series: Classics of Soviet Mathematics |
| Physical Information: 1.12" H x 6.28" W x 9.6" (1.67 lbs) 444 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: A.D. Alexandrov is considered by many to be the father of intrinsic geometry, second only to Gauss in surface theory. That appraisal stems primarily from this masterpiece--now available in its entirely for the first time since its 1948 publication in Russian. Alexandrov's treatise begins with an outline of the basic concepts, definitions, and results relevant to intrinsic geometry. It reviews the general theory, then presents the requisite general theorems on rectifiable curves and curves of minimum length. Proof of some of the general properties of the intrinsic metric of convex surfaces follows. The study then splits into two almost independent lines: further exploration of the intrinsic geometry of convex surfaces and proof of the existence of a surface with a given metric. The final chapter reviews the generalization of the whole theory to convex surfaces in the Lobachevskii space and in the spherical space, concluding with an outline of the theory of nonconvex surfaces. Alexandrov's work was both original and extremely influential. This book gave rise to studying surfaces in the large, rejecting the limitations of smoothness, and reviving the style of Euclid. Progress in geometry in recent decades correlates with the resurrection of the synthetic methods of geometry and brings the ideas of Alexandrov once again into focus. This text is a classic that remains unsurpassed in its clarity and scope. |