Two reports on harmonic maps

Harmonic maps between Riemannian manifolds are solutions of systems of partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, delta-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kahlerian manifolds. Standard references for this subject are two 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 source of reference, providing an organized exposition of results spread throughout more than 800 papers. Foreword......Page 6 TABLE OF CONTENTS......Page 8 1. Introduction ......Page 14 2. Operations on vector bundles ......Page 17 3. Harmonic maps ......Page 21 4. Composition properties ......Page 27 5. Maps into manifolds of nonpositive (< 0) curvature ......Page 31 6. The existence theorem for Riem N < 0 ......Page 35 7. Maps into flat manifolds ......Page 42 8. Harmonic maps between spheres ......Page 45 9 Holomorphic maps ......Page 51 10 Harmonic maps of a surface ......Page 55 11. Harmonic maps between surfaces ......Page 61 12. Harmonic maps of manifolds with boundary ......Page 68 References ......Page 74 1. Introduction ......Page 82 2. Harmonic maps ......Page 84 3. Regularity theory ......Page 92 4. Maps of Kahler manifolds ......Page 102 5. Maps of surfaces ......Page 113 6. Second variation ......Page 124 7. Twistor constructions ......Page 133 8. Maps into groups and Grassmannians ......Page 144 9. Maps into loop spaces ......Page 154 10. Maps into spheres ......Page 161 11. Non-compact manifolds ......Page 171 12 - Manifolds with boundary ......Page 184 References ......Page 199 III. NOT ANOTHER REPORT ON HARMONIC MAPS ......Page 222 IV. INDEX ......Page 224 This volume contains two reports on harmonic maps, published in 1978 and 1988 by James Eells and Luc Lemaire, which have become standard references for this subject. A brief supplement reports on some recent developments in the theory. Harmonic maps between Riemannian manifolds are solutions of systems of partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, delta-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kahlerian manifolds.;Standard references for this subject are two 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 source of reference, providing an organized exposition of results spread throughout more than 800 papers 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, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian 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.