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The contemplation of the atlas of an airline company always offers us something puzzling: the trajectories of the airplanes look curved, which goes against our basic intuition, according to which the shortest path is a straight line. One of the reasons for this paradox is nothing but a simple geometrical fact: on the one hand our earth is round and on the other hand the shortest path on a sphere is an arc of great circle: a curve whose projection on a geographical map rarely coincides with a straight line. Actually, choosing the trajectories of airplanes is a simple illustration of a classical variational problem in differential geometry: finding. | CAMBRIDGE TRACTS IN MATHEMATICS 150 HARMONIC MAPS CONSERVATION LAWS AND MOVING FRAMES FREDERIC HÉLEIN CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE TRACTS IN MATHEMATICS General Editors B. BOLLOBAS W. FULTON A. KATOK F. KIRWAN P. SARNAK 150 Harmonic maps conservation laws and moving frames Second edition This page intentionally left .
