Vanishing results from Lichnerowicz Laplacian on complete K\"{a}hler manifolds and applications

In this paper, we show several rigidity results for harmonic $(p,q)$-forms in complete K"{a}hler manifolds. We also give several applications to study non-compact K"{a}hler manifolds with parallel Bochner tensor or quaternion K"{a}hler manifolds. Our results are natural extensions of Petersen and Wink’s results in \cite{PW21, PW} in the setting of complete, non-compact K"{a}hler manifolds.