Abstract
In this chapter we shall study the integral ∫ s K of the Gaussian curvature over a compact oriented 2-surface S. We shall see that (1/2π) ∫ s K always turns out to be an integer, the Euler characteristic of S. This is the 2-dimensional version of the Gauss-Bonnet theorem. A similar result is valid in all higher even dimensions but the computations are less transparent so we shall be content with a few comments about this more general case at the end of the chapter.
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). The Gauss-Bonnet Theorem. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_21
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_21
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
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