Vanishing results from Lichnerowicz Laplacian on complete Kähler manifolds and applications

2022/02/06 by Gunhee Cho, Nguyen Thac Dung, Cho, Gunhee +1 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2202.02700

openalex publication_date 2022/02/06 · openalex created_date 2022/02/24 · openalex updated_date 2026/07/28

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 \citePW21, PW in the setting of complete, non-compact Kähler manifolds.

Cited by

• Weitzenböck-Bochner-Kodaira formulas with quadratic curvature terms
• Refined Kato type inequalities and new vanishing theorems on complete Kähler and quaternionic Kähler manifolds

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