A Concise Guide Toponogov, Victor A. creator author. Rovenski, Vladimir Y. editor. SpringerLink (Online service) text xxu 2006 monographic eng

electronic

electronic resource

access XII, 206 p. 70 illus. online resource. 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. 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. by Victor A. Toponogov ; edited by Vladimir Y. Rovenski. MATHEMATICS GLOBAL DIFFERENTIAL GEOMETRY MATHEMATICS DIFFERENTIAL GEOMETRY 516.36 9780817644024 99780817644024 http://dx.doi.org/10.1007/b137116 http://dx.doi.org/10.1007/b137116 100301 20260521092024.0 978-0-8176-4402-4