Lectures on Harmonic Maps
نویسندگان
چکیده
§1 Background and Setup Let M be an m-dimensional, compact, Riemannian manifold endowed with the metric dsM = gij dx i dx , where {x, x, · · · , x} is a local coordinate system of M. Suppose N is an n-dimensional, complete, Riemannian manifold with metric given by dsN = hαβ du α du , where {u, u, · · · , u} is a local coordinate system of N. Let f : M → N be a C mapping from M into N . Definition 1.1. The energy density of f is defined to be the trace of the pullback of the metric of N by f . It is denoted by e(f) = trMf (dsN ). The total energy of f us defined by the integral of the energy density over M, denoted by
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