2010 | OriginalPaper | Chapter
Local Properties of Surfaces
Author : Laurent Younes
Published in: Shapes and Diffeomorphisms
Publisher: Springer Berlin Heidelberg
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In this chapter, we start discussing representations that can be associated to three-dimensional shapes, where surfaces now replace curves. For this reason, we start with basic definitions and results on the theory of surfaces in ℝ
3
. Although some parts are redundant with the abstract discussion of submanifolds that is provided in Appendix B, we have chosen to provide a more elementary presentation here, very close to [64], to ensure that this important section can be read independently.