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Let $X$ be a smooth projective complex variety with an ample line bundle $L$,and let $D$ be a simple normal crossing divisor. We establish theKobayashi-Hitchin correspondence between tame harmonic bundles on $X-D$ and$\mu_L$-stable parabolic $\lambda$-flat bundles with trivial characteristicnumbers on $(X,D)$. Especially, we obtain the quasiprojective version of theCorlette-Simpson correspondence between flat bundles and Higgs bundles.Comment: Some arguments are simplifie

Kobayashi–Hitchin correspondence for tame harmonic bundles II