Harmonic maps in unfashionable geometries

Harmonic maps in unfashionable geometries

Many topics in integrable surface geometry may be unified by application of the highly developed theory of harmonic maps of surfaces into (pseudo-)Riemannian symmetric spaces. On the one hand, such harmonic maps comprise an integrable system with spectral deformations, algebro-geometric solutions and dressing actions of loop groups generated by Bäcklund transforms [5], [6], [14], [21], [24]. On...

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Harmonic Maps and Biharmonic Maps

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

Lectures on Harmonic Maps

§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 . Definiti...