Geometry and dynamics II: geodesic flow on a surface

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter XII in Geometry Revealed, 2010, pp 739-783 from Springer

Abstract: Abstract We will be interested in the geometry on a surface subj Surface (not of a surface, see in Sect. VI.2 for an explanation of this important distinction) and simultaneously in mechanics subj 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 subj Ellipsoid 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.

Keywords: Short Path; Constant Curvature; Riemannian Geometry; Negative Curvature; Topological Entropy (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-70997-8_12

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