Abstract
All the properties of curves that we have discussed so far are ‘local’: they depend only on the behaviour of a curve near a given point and not on the ‘global’ shape of the curve. Proving global results about curves often requires concepts from topology, in addition to the calculus techniques we have used in the first two chapters of this book. Since we are not assuming that readers of this book have extensive familiarity with topological ideas, we will not be able to give complete proofs of some of the global results about curves that we discuss in this chapter.
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© 2010 Springer-Verlag London Limited
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Pressley, A. (2010). Global properties of curves. In: Elementary Differential Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84882-891-9_3
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DOI: https://doi.org/10.1007/978-1-84882-891-9_3
Publisher Name: Springer, London
Print ISBN: 978-1-84882-890-2
Online ISBN: 978-1-84882-891-9
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