Synthetic Differential Geometry
by Anders Kock
Publisher: Cambridge University Press 2006
Number of pages: 241
Synthetic Differential Geometry is a method of reasoning in differential geometry and calculus, where use of nilpotent elements allows the replacement of the limit processes of calculus by purely algebraic notions. In this second edition of Kock's classical text, many notes have been included commenting on new developments.
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by Liviu I. Nicolaescu - University of Notre Dame
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
by M. Desbrun, P. Schroeder, M. Wardetzky - Columbia University
This new and elegant area of mathematics has exciting applications, as this text demonstrates by presenting practical examples in geometry processing (surface fairing, parameterization, and remeshing) and simulation (of cloth, shells, rods, fluids).
by Aleks Kleyn, Alexandre Laugier - arXiv
In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Contents: Preface; Minkowski Space; Examples of Minkowski Space.
by Brian White - arXiv
The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.