Two Reports on Harmonic Maps

Two Reports on Harmonic Maps

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Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, Iƒ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and KAchlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.Therefore alt;jagt; is harmonic, and has constant energy density Note also that alt;jagt; covers a harmonic map Pp~l x P*~1 -Ar Paquot;~1. ... M. Thus we have an induced map $agt; of the orbit spaces, and a commutative diagram t N The tension field of such a map alt;/agt; is itself equivariant; and alt;jagt; is harmonic if and only if it is an extremal of the energy with respect to all compactly supported equivariant variations [99, 206 ].

Title:Two Reports on Harmonic Maps
Author: James Eells, Luc Lemaire
Publisher:World Scientific - 1995

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