02537nam a22003615i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024002500137082001500162100003400177245015100211264004600362300004400408336002600452337002600478338003600504347002400540505018100564520111900745650001701864650003401881650001701915650002701932700003501959710003401994773002002028776003602048856009102084978-0-8176-4402-4DE-He21320260521092024.0cr nn 008mamaa100301s2006    xxu|    s    |||| 0|eng d  a9780817644024  a997808176440247 a10.1007/b1371162doi04a516.362231 aToponogov, Victor A.eauthor.10aDifferential Geometry of Curves and Surfacesh[electronic resource] :bA Concise Guide /cby Victor A. Toponogov ; edited by Vladimir Y. Rovenski. 1aBoston, MA :bBirkhäuser Boston,c2006.  aXII, 206 p. 70 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aTheory of Curves in Three-dimensional Euclidean Space and in the Plane -- Extrinsic Geometry of Surfaces in Three-dimensional Euclidean Space -- Intrinsic Geometry of Surfaces.  aThe 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. 0aMATHEMATICS. 0aGLOBAL DIFFERENTIAL GEOMETRY.14aMATHEMATICS.24aDIFFERENTIAL GEOMETRY.1 aRovenski, Vladimir Y.eeditor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978081764384340uhttp://dx.doi.org/10.1007/b137116zVer el texto completo en las instalaciones del CICY