Advances in Discrete Differential Geometry
by Alexander I. Bobenko (ed.)
Publisher: Springer 2016
Number of pages: 439
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.
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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.
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We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
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Differential geometry is deceptively simple. It is surprisingly easy to get the right answer with informal symbol manipulation. We use computer programs to communicate a precise understanding of the computations in differential geometry.