Two Reports on Harmonic Maps
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, I-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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