Abstract
The most deeply rooted geometrical properties of a surface are its topological ones: these are preserved under all homeomorphisms of the surface. Hence also, they are preserved under all deformations. (Some examples of deformations of surfaces were studied at the end of Chapter 11.) There is a broader class of properties that are intimately bound up with the geometry of the surface and that are preserved under a large subclass of homeomorphisms. These are ones that Gauss discovered, and which we will now explore.
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Casey, J. (1996). Intrinsic Geometry of a Surface. In: Exploring Curvature. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-80274-3_13
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DOI: https://doi.org/10.1007/978-3-322-80274-3_13
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-06475-4
Online ISBN: 978-3-322-80274-3
eBook Packages: Springer Book Archive