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.
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19.5 References
Anderson, J.W. 2005 Hyperbolic Geometry, 2nd edn., Springer Undergraduate Mathematics Series, Springer, London.
Beardon, A.F. 1995 The Geometry of Discrete Groups, corrected reprint of 1983 original, Graduate Texts in Mathematics, Springer, New York.
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(2007). Differential Geometry of Surfaces. In: Worlds Out of Nothing. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84628-633-9_19
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DOI: https://doi.org/10.1007/978-1-84628-633-9_19
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