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Geometry Revealed pp 739–783Cite as

Geometry and dynamics II: geodesic flow on a surface

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Abstract

We will be interested in the geometry on a surface (not of a surface, see in Sect. VI.2 for an explanation of this important distinction) and simultaneously in mechanics on it (Arnold, 1978). There are at least three motivations for this. First motivation: our planet is to a first approximation a surface, rather well described as an ellipsoid of revolution of revolution (see below). It is thus important to comprehend the nature of the geometry of such a surface; a typical question: what is the shortest path from one point to another? This is the aspect of living on a surface. Now physicists – who are interested in much more complicated mechanical systems – need to study simple systems because these provide good tests for general hypotheses.

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Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, IHÉS, Bures-sur-Yvette, 35 route des Chartres, 91440, Bures-sur-Yvette, France

    Marcel Berger

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Berger, M. (2010). Geometry and dynamics II: geodesic flow on a surface. In: Geometry Revealed. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70997-8_12

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