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Chapters: Gauss-bonnet Theorem, Riemannian Connection on a Surface, Darboux Frame, Introduction to Systolic Geometry, Gauss-codazzi Equations, Gaussian Curvature, Second Fundamental Form, Ruled Surface, Principal Curvature, Mean Curvature, Minimal Surface, Systoles of Surfaces, First Fundamental Form, Saddle Point, Theorema Egregium, Loewner's Torus Inequality, Pu's Inequality, First Hurwitz Triplet, Gauss Map, Klein Quartic, Macbeath Surface, Hurwitz Quaternion Order, Developable Surface, Filling Area Conjecture, Euler's Theorem, Umbilical Point, Bolza Surface, Geodesic Curvature, Asymptotic Curve, Weingarten Equations, Tangential Developable, Bertrand-diquet-puiseux Theorem, Dupin Indicatrix, Zoll Surface, Ridge, Clairaut's Relation, Tangent Developable, Liberman's Lemma, Hyperbolic Point. Source: Wikipedia. Pages: 196. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, first studied in depth by Carl Friedrich Gauss (1825-1827), who showed that curvature was an intrinsic property of a surface, independent of its isometric embedding in Euclidean space. Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves. An important role in their study has been played by Lie groups (in the spirit of the Erlangen program), namel...More: http://booksllc.net/?id=15513875 ... Read more |
