Worlds Out of Nothing pp 203-217 | Cite as

# Differential Geometry of Surfaces

Chapter

## Abstract

Let us consider a surface in space, given by an equation of the form *F* (*x, y, z*) = 0. We shall assume we have a map from a region of the plane, with coordinates (*u, v*) onto part of the surface, and that we can differentiate this map as often as we like. We assume that at each point of the surface the directions u-increasing and *v*-increasing are distinct.

## Keywords

Great Circle Euclidean Geometry Real Point Geodesic Triangle Limit Circle
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## 19.5 References

- [2]Anderson, J.W. 2005
*Hyperbolic Geometry*, 2nd edn., Springer Undergraduate Mathematics Series, Springer, London.Google Scholar - [9]Beardon, A.F. 1995
*The Geometry of Discrete Groups*, corrected reprint of 1983 original, Graduate Texts in Mathematics, Springer, New York.Google Scholar - [15]Berger, M. 1987
*Geometry I*, tr. from French by M. Cole and S. Levy, Universitext, Springer, Berlin.zbMATHGoogle Scholar - [16]Berger, M. 1987
*Geometry II*, tr. from French by M. Cole and S. Levy, Universitext, Springer, Berlin.zbMATHGoogle Scholar - [168]Morgan, F. 1998
*Riemannian Geometry*, 2nd. edn., A K Peters Ltd., Wellesley MA.zbMATHGoogle Scholar - [227]Struik, D.J. 1988
*Lectures on Classical Differential Geometry*, 2nd edn., Dover Publications Inc., New York.zbMATHGoogle Scholar

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