Abstract
In this paper, we show several rigidity results for harmonic -forms in complete Kähler manifolds. We also give several applications to study non-compact Kähler manifolds with parallel Bochner tensor or quaternion Kähler manifolds. Our results are natural extensions of Petersen and Wink's results in \cite{PW21, PW} in the setting of complete, non-compact Kähler manifolds.
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