Some curvature properties of complex surfaces
Some curvature properties of complex surfaces
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复杂曲面的一些曲率性质
DOI：
10.1007/bf01760974
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发表时间：
1982
影响因子：
1
通讯作者：
I. Vaisman
中科院分区：
文献类型：
--
作者：
I. Vaisman
摘要在本文中，我们正在研究复二维埃尔米特流形的曲率性质，特别是在紧的情况下。为了做到这一点，我们从这样一个流形的基本形式是可积的这一评论开始，并且我们使用与局部共形凯勒流形的类比，这是从这一评论得出的。其中，当黎曼曲率张量满足Kähler对称性或Hermitian曲率张量满足黎曼比安奇恒等式时，紧致Hermitian曲面是Kähler曲面，常截面曲率的紧致Hermitian曲面是平坦的Kähler曲面;具有非负非全同零Hermite对分曲率的紧致Hermite曲面M具有消失的多属，c1（M）≠ 0，不存在例外曲线，具有特殊度量的紧致Hermite曲面，正积分黎曼标量曲率的复生成为零等.
SummaryIn this paper, we are investigating curvature properties of complex two-dimensional Hermitian manifolds, particularly in the compact case. To do this, we start with the remark that the fundamental form of such a manifold is integrable, and we use the analogy with the locally conformal KÄhler manifolds, which follows from this remark. Among the obtained results, we have the following: a compact Hermitian surface for which either the Riemannian curvature tensor satisfies the KÄhler symmetries or the Hermitian curvature tensor satisfies the Riemannian Bianchi identity is KÄhler; a compact Hermitian surface of constant sectional curvature is a flat KÄhler surface; a compact Hermitian surface M with nonnegative nonidentical zero holomorphie Hermitian bisectional curvature has vanishing plurigenera, c1(M) ⩾ 0, and no exceptional curves; a compact Hermitian surface with distinguished metric, and positive integral Riemannian scalar curvature has vanishing plurigenera, etc.