Harmonic Maps Into Homogeneous Spaces
This book is concerned with harmonic maps into homogeneous spaces and focuses upon maps of Riemann surfaces into flag manifolds, to bring results of 'twistor methods' for symmetric spaces into a unified framework by using the theory of compact Lie groups and complex differential geometry.
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A(gC analysis applications automorphism boundary called canonical connection Chapter choice choose Claim compact complex structure condition conformal conjugation consider containing contradiction defined definition denote direct sum distinct irreducible summands equi-harmonic equivalent established examples f-holomorphic flag manifolds follows full flag manifold function Further geometry H Brezis h invariant harmonic maps hence holomorphic holomorphic map homogeneous space horizontal f-structure identity implies induced integrable invariant metrics Lemma Let G Lie algebra Lie group Lions maximal torus methods minimal mutually Nonlinear partial differential Note obtain operators orbit orthogonal partial differential equations positive root problems projection Proof properties proves provides reductive homogeneous space reductive splitting respect result Riemann surface root spaces satisfies shows simple roots SU(n sub-algebra subgroup subset sufficient Suppose symmetric spaces Theorem theory trivial twistor University vector Volume αε