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Differential Geometry of Curves and Surfaces : A Concise Guide /

By: Toponogov, Victor A [author.].
Contributor(s): Rovenski, Vladimir Y [editor.2] | SpringerLink (Online service)0.
Material type: materialTypeLabelBookPublisher: Boston, MA : Birkh�user Boston, 2006. Description: XIV, 206 p. 70 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817644024.Subject(s): Mathematics | Differential geometry.1 | Mathematics.2 | Differential Geometry.1DDC classification: 516.36 Online resources: Click here to access online
Contents:
Theory of Curves in Three-dimensional Euclidean Space and in the Plane -- Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space -- Intrinsic Geometry of Surfaces.
In: Springer eBooks0Summary: The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels. Key topics and features: * Covers central concepts including curves, surfaces, geodesics, and intrinsic geometry * Substantive material on the Aleksandrov global angle comparison theorem, which the author generalized for Riemannian manifolds (a result now known as the celebrated Toponogov Comparison Theorem, one of the cornerstones of modern Riemannian geometry) * Contains many nontrivial and original problems, some with hints and solutions This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK7796
Total holds: 0

Theory of Curves in Three-dimensional Euclidean Space and in the Plane -- Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space -- Intrinsic Geometry of Surfaces.

The study of curves and surfaces forms an important part of classical differential geometry. Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels. Key topics and features: * Covers central concepts including curves, surfaces, geodesics, and intrinsic geometry * Substantive material on the Aleksandrov global angle comparison theorem, which the author generalized for Riemannian manifolds (a result now known as the celebrated Toponogov Comparison Theorem, one of the cornerstones of modern Riemannian geometry) * Contains many nontrivial and original problems, some with hints and solutions This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry.

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