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.
General
| Imprint: |
Crc Press
|
| Country of origin: |
United Kingdom |
| Series: |
Classics of Soviet Mathematics |
| Release date: |
July 2005 |
| First published: |
March 2005 |
| Editors: |
S.S. Kutateladze
|
| Dimensions: |
234 x 156 x 28mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
444 |
| ISBN-13: |
978-0-415-29802-5 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
General
|
| LSN: |
0-415-29802-4 |
| Barcode: |
9780415298025 |
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