Abstract
A regular surface looks like a plane if one zooms sufficiently in near any point, but if one zooms back out, it might curve and bend through the ambient \(\mathbb{R}^{3}\). That’s what makes differential geometry so much richer than Euclidean geometry.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We recommend [1] for an elementary excursion into the theory of knots.
Recommended Excursions
C. Adams, The Knot Book, American Mathematical Society, 2004.
M. Beeson, Notes on Minimal Surfaces, preprint, 2007, http://michaelbeeson.com/research/papers/IntroMinimal.pdf
V. Blåsjö, The Isoperimetric Problem, American Mathematical Monthly. 112, No. 6 (2005), 526–566.
D. DeTurck, H. Gluck, D. Pomerleano, and D. Shea Vick, The Four Vertex Theorem and Its Converse, Notices of the AMS. 54, No. 2 (2007), 192–206.
R. Osserman, A Survey of Minimal Surfaces, Dover (1986).
S. Sawin, South Point Chariot: An Invitation to Differential Geometry, preprint, 2015.
D. Sobel, Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, Walker Books, 2007.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Tapp, K. (2016). The Curvature of a Surface. In: Differential Geometry of Curves and Surfaces. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-39799-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-39799-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39798-6
Online ISBN: 978-3-319-39799-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)