Abstract
Despite the effort that might be required to master the constructions of the previous chapter, the core concerns of Riemannian geometry are traditional ones: length, angles, curvature, etc. Indeed, the way we view the underlying set of spatial “points” in Riemannian geometry is not much different from the way that Euclid described them over one thousand years ago.
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Notes
- 1.
Quoted in H. Geiges, An Introduction to Contact Topology, Cambridge University Press, New York, 2008, p. ix.
References
Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, New York (1989)
Bennequin, D.: Entrelacements et équations de Pfaff. Third Schnepfenried geometry conference, vol. 1, pp. 87–161 (Schnepfenried, 1982); Astérisque, vol. 107–108. Société mathématique de France, Paris (1983)
Burke, W.L.: Applied Differential Geometry. Cambridge University Press, New York (1985)
Folland, G.B.: Introduction to Partial Differential Equations, 2nd edn. Princeton University Press, Princeton (1995)
Geiges, H.: A brief history of contact geometry and topology. Expo. Math. 19(1), 25–53 (2001)
Geiges, H.: Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117–123 (2005)
Geiges, H.: An Introduction to Contact Topology. Cambridge University Press, New York (2008)
Giaquinta, M., Hildebrandt, S.: Calculus of Variations II. Springer, New York (1996)
Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, vols. 1 and 2. Wiley, New York (1963, 1969)
Libermann, P., Marle, C.-M.: Symplectic Geometry and Analytical Mechanics. D. Reidel, Boston (1987)
Lie, S.: Geometrie der Berührungstransformationen. B.G. Teubner, Leipzig (1896)
Lie, S., Engel, F.: Theorie der Transformationsgruppen, vol. 3. B.G. Teubner, Leipzig (1888–1893)
Warner, F.W.: Foundations of Differentiable Manifolds and Lie Groups. Springer, New York (1983)
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McInerney, A. (2013). Contact Geometry. In: First Steps in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7732-7_6
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