The Injectivity Theorem on a Non-Compact Kähler Manifold

Abstract

In this paper, we establish an injectivity theorem on a weakly pseudoconvex Kähler manifold X with negative sectional curvature. For this purpose, we develop the harmonic theory in this circumstance. The negative sectional curvature condition is usually satisfied by the manifolds with hyperbolicity, such as symmetric spaces, bounded symmetric domains in Cn, hyperconvex bounded domains, and so on.

Keywords

• non-compact Kähler manifold
• Hodge decomposition
• harmonic differential form
• Hilbert space