Hermitian symmetric space, flat bundle and holomorphicity criterion

2016/03/08 by Hassan Azad, Azad, Hassan, Indranil Biswas +5
Mathematics · #32L05 #32M15 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32L05 #msc:32M15 #msc:53C55

paper · pdf · doi:10.48550/arxiv.1603.02387

Final version

arxiv created 2016/03/08 · arxiv updated 2016/03/09

Abstract

Let K\backslash G be an irreducible Hermitian symmetric space of noncompact type and Γ ⊂ G a closed torsionfree discrete subgroup. Let X be a compact Kähler manifold and ρ : π₁(X, x₀) \longrightarrow Γ a homomorphism such that the adjoint action of ρ(π₁(X, x₀)) on Lie(G) is completely reducible. A theorem of Corlette associates to ρ a harmonic map X \longrightarrow K\backslash G/Γ. We give a criterion for this harmonic map to be holomorphic. We also give a criterion for it to be anti--holomorphic.

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