Harmonic Maps Into Homogeneous Spaces

by Malcolm Black

Overview

Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.

Product Details

ISBN-13:	9781351441612
Publisher:	CRC Press
Publication date:	05/04/2018
Series:	Chapman & Hall/CRC Research Notes in Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	104
File size:	3 MB

About the Author

Malcolm Black

Table of Contents

1. Introduction 2. Homogeneous Geometry 3. f-Structures and f-Holomorphic Maps 4. f-Structures on Reductive Homogeneous Spaces 5. Equi-Harmonic Maps 6. Classification of Horizontal f-Structures on Flag Manifolds 7. Integrable f-Holomorphic Orbits on Flags 8. Equi-Minimal Maps of Riemann Surfaces to Full Flag Manifolds