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Symmetry
Volume 13
Issue 11
10.3390/sym13112222
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Article

The Injectivity Theorem on a Non-Compact Kähler Manifold

by
Jingcao Wu
School of Mathematical Sciences, Shanghai University of Finance and Economics, Shanghai 200433, China
Symmetry 2021, 13(11), 2222; https://doi.org/10.3390/sym13112222
Submission received: 20 October 2021 / Revised: 8 November 2021 / Accepted: 9 November 2021 / Published: 20 November 2021
(This article belongs to the Special Issue Functional Equations and Inequalities 2021)
Versions Notes

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

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MDPI and ACS Style

Wu, J. The Injectivity Theorem on a Non-Compact Kähler Manifold. Symmetry 2021, 13, 2222. https://doi.org/10.3390/sym13112222

AMA Style

Wu J. The Injectivity Theorem on a Non-Compact Kähler Manifold. Symmetry. 2021; 13(11):2222. https://doi.org/10.3390/sym13112222

Chicago/Turabian Style

Wu, Jingcao. 2021. "The Injectivity Theorem on a Non-Compact Kähler Manifold" Symmetry 13, no. 11: 2222. https://doi.org/10.3390/sym13112222

APA Style

Wu, J. (2021). The Injectivity Theorem on a Non-Compact Kähler Manifold. Symmetry, 13(11), 2222. https://doi.org/10.3390/sym13112222

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