![]() ![]() Riemann curvature tensor, and a second proof of Gauss's Theorema Egregium. Gauss's formulas, Christoffel symbols, Gauss and Codazzi-Mainardi equations, Intrinsic metric and isometries of surfaces, Gauss's Theorema Egregium,īrioschi's formula for Gaussian curvature. Ratio of areas, and products of principal curvatures. Interpretations of Gaussian curvature as a measure of local convexity, Gaussian curvature, Gauss map, shape operator, coefficients of the firstĪnd second fundamental forms, curvature of graphs. Torsion, Frenet-Seret frame, helices, spherical curves. The four vertex theorem, Shur's arm lemma, isoperimetric inequality. Osculating circle, Kneser's Nesting Theorem, total curvature, convex curves. General definition of curvature using polygonal approximations (Fox-Milnor's theorem).Ĭurves of constant curvature, the principal normal, signed curvature, turning angle, ![]() Isometries of Euclidean space, formulas for curvature of smooth regular curves. Nº de ref.Basics of Euclidean Geometry, Cauchy-Schwarz inequality.ĭefinition of curves, examples, reparametrizations, length, Cauchy's integral formula, curves of constant width. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. ![]() nach der Bestellung gedruckt Neuware - Printed after ordering - This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. "Sobre este título" puede pertenecer a otra edición de este libro.ĭescripción Buch. This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980.
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