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For this metric, we first establish the vanishing of its \\(L^2\\)-Dolbeault cohomology outside the middle degree: \\(\\dim H^{p,q}_2(\\Omega)=0\\) if \\(p+q\\ne n\\), while \\(\\dim H^{p,q}_2(\\Omega)=\\infty\\) if \\(p+q=n\\). We also prove that the metric has \\(C^\\infty\\)-bounded geometry. Using this analytic property, we obtain several rigidity results. 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For this metric, we first establish the vanishing of its \\(L^2\\)-Dolbeault cohomology outside the middle degree: \\(\\dim H^{p,q}_2(\\Omega)=0\\) if \\(p+q\\ne n\\), while \\(\\dim H^{p,q}_2(\\Omega)=\\infty\\) if \\(p+q=n\\). We also prove that the metric has \\(C^\\infty\\)-bounded geometry. Using this analytic property, we obtain several rigidity results. 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