Vanishing results from Lichnerowicz Laplacian on complete Kähler manifolds and applications

Abstract

In this paper, we show several rigidity results for harmonic $(p,q)$-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.

arXiv commentarXiv admin note: text overlap with arXiv:2111.07496; text overlap with arXiv:2105.09290 by other authors, to appear in Journal of Mathematical Analysis and Applications