دانلود کتاب Harmonic Maps Into Homogeneous Spaces

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Content: Part 1 Introduction: harmonic maps, two dimensional domains, maps into symmetric spaces, flag manifolds, summary of contents. Part 2 Homogeneous geometry: generalities, reductive splittings, distinct reductive summands, invariant tensors, the Levi-Civita connection, roots, Noether's theorem. Part 3 f-structures and f-holomorphic maps. Part 4 f-structures on reductive homogeneous spaces: f-structures and metrics, horizontality, example - SU(n) flag manifolds. Part 5 Equi-harmonic maps. Part 6 Classification of horizontal f-structures on flag manifolds: algebraic preliminaries, reduction to the irreducible case, characterization of irreducible f-structures I, characterization of irreducible f-structures II, summary and examples. Part 7 Integrable f-holomorphic orbits on flags: integrable orbits are hermitian symmetric, orbits in the full flag manifold, case 6.13B., case 6.13A., concluding remarks. Part 8 Equi-minimal maps of Riemann surfaces to full flag manifolds: equi-minimal maps are horizontal holomorphic, branched horizontal curves in full flags.