By E. Loubeau, S. Montaldo
This quantity comprises the complaints of a convention held in Cagliari, Italy, from September 7-10, 2009, to have fun John C. Wood's sixtieth birthday. those papers replicate the numerous features of the speculation of harmonic maps and its hyperlinks and connections with different subject matters in Differential and Riemannian Geometry. lengthy experiences, one on consistent suggest curvature surfaces by way of F. Pedit and the opposite at the building of harmonic maps by means of J. C. wooden, open the lawsuits. those are through a mixture of surveys on Prof. Wood's forte: Lagrangian surfaces, biharmonic maps, in the community conformally Kahler manifolds and the DDVV conjecture, in addition to numerous learn papers on harmonic maps. different learn papers within the quantity are dedicated to Willmore surfaces, Goldstein-Pedrich flows, touch pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf version, the Compact help precept and the curvature of surfaces
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Extra info for Harmonic Maps and Differential Geometry: A Harmonic Map Fest in Honour of John C. Wood's 60th Birthday September 7-10, 2009 Cagliari, Italy
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To see how this might play out, we ﬁrst consider a CMC immersion f : M → R3 of a compact Riemann surface M of genus g for which the family of ﬂat connections (8) has abelian monodromy representations ρλ : π1 (M, p0 ) → SL(2, C). In this case, ρλ : H1 (M, Z) → SL(2, C) factors through homology and since the Abel map A : M → Jac(M ) based at p0 ∈ M induces the isomorphism A∗ : H1 (M, Z) → H1 (Jac(M ), Z) ∼ = π1 (Jac(M )) on homology, we obtain a family of ﬂat connections d˜λ on the Jacobian which, by construction, pulls back via the Abel map to dλ .
Harmonic Maps and Differential Geometry: A Harmonic Map Fest in Honour of John C. Wood's 60th Birthday September 7-10, 2009 Cagliari, Italy by E. Loubeau, S. Montaldo