Discrete Differential Geometry: An Applied Introduction
by M. Desbrun, P. Schroeder, M. Wardetzky
Publisher: Columbia University 2008
Number of pages: 103
This new and elegant area of mathematics has exciting applications, as this course demonstrates by presenting practical examples in geometry processing (surface fairing, parameterization, and remeshing) and simulation (of cloth, shells, rods, and fluids).
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by Paul Loya - Binghamton University
This is a lecture-based class on the Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
by Thomas E. Cecil, Shiing-shen Chern - Cambridge University Press
Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
by Thomas Banchoff, Terence Gaffney, Clint McCrory - Pitman Advanced Pub. Program
Gauss mappings of plane curves, Gauss mappings of surfaces, characterizations of Gaussian cusps, singularities of families of mappings, projections to lines, focal and parallel surfaces, projections to planes, singularities and extrinsic geometry.
by Ivan Kolar, Peter W. Michor, Jan Slovak - Springer
A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.