General covariance and harmonic maps

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.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

stable exponentially harmonic maps between finsler manifolds

Harmonic maps and soliton theory

The study of harmonic maps of a Riemann sphere into a Lie group or, more generally, a symmetric space has been the focus for intense research by a number of Differential Geometers and Theoretical Physicists. As a result, these maps are now quite well understood and are seen to correspond to holomorphic maps into some (perhaps infinite-dimensional) complex manifold. For more information on this ...

Constructing Buildings and Harmonic Maps

In a continuation of our previous work [20], we outline a theory which should lead to the construction of a universal pre-building and versal building with a φ-harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group SL3. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for S...