Abstract
(zlM is the Laplace-Beltrami operator on M.) In local coordinates on JV, (1.2) takes the form AMu = r(u)(Vu,Vu) (1.3) with a bilinear form T involving the Christoffel symbols of the metric g on JV. Again, if M cz and if, in particular, JV = Ŝ cz R (n = £ + 1), (1.3) takes the following simple form Au = u\Wu\. The notion of harmonic map generalizes the concepts of closed geodesic (for M = S) and harmonic function (for JV = R).
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