The $$\partial \overline \partial $$-Bochner Formulas for Holomorphic Mappings between Hermitian Manifolds and Their Applications
The $$\partial \overline \partial $$-Bochner Formulas for Holomorphic Mappings between Hermitian Manifolds and Their Applications
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DOI：
10.1007/s10473-021-0515-4
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发表时间：
2019-10
影响因子：
1
通讯作者：
Kai Tang
中科院分区：
文献类型：
--
作者：
Kai Tang
本文给出了厄米特流形之间全纯映射的几个-Bochner公式。作为应用，我们证明了一些Schwarz引理估计，以及一些刚性和退化定理。例如，我们证明了紧致Hermite流形不存在非常数全纯映射，其中正(？)非负)ℓ-Second Ricci曲率到非正的Hermite流形。负)实对分曲率。这些定理将L.Ni最近在Kähler流形上证明的结果推广到Hermite流形上。我们还得到了厄米特流形之间的全纯映射的一个积分不等式。
In this paper, we derive some-Bochner formulas for holomorphic maps between Hermitian manifolds. As applications, we prove some Schwarz lemma type estimates, and some rigidity and degeneracy theorems. For instance, we show that there is no non-constant holomorphic map from a compact Hermitian manifold with positive (resp. non-negative)ℓ-second Ricci curvature to a Hermitian manifold with non-positive (resp. negative) real bisectional curvature. These theorems generalize the results [5, 6] proved recently by L. Ni on Kähler manifolds to Hermitian manifolds. We also derive an integral inequality for a holomorphic map between Hermitian manifolds.