论文标题
Griffiths负矢量束和准富奇的总空间的总空间的曲率
Curvature of the total space of a Griffiths negative vector bundle and quasi-Fuchsian space
论文作者
论文摘要
对于Hermitian歧管$ M $上的Holomorthic Vector Bundle $ e $ e $，有两个重要的曲率积极概念，Griffiths的积极性和Nakano的积极性。我们研究这些阳性的结果和相关估计。如果$ e $对kähler歧管的谷物负面影响，那么总空间$ e $就有一个kähler指标，我们计算曲率并证明沿着重言式方向的曲率的非阳性。 Nakano阳性可以作为中Nakano曲率操作员的阳性配方，我们给出了与Nakano阳性直接图像束相关的Nakano曲率算子。 As applications we construct a mapping class group invariant Kähler metric on the quasi-Fuchsian space QF$(S)$, which extends the Weil-Petersson metric on the Teichmüller space $\mathcal{T}(S)\subset {\rm QF}(S)$, and we obtain estimates for the Nakano curvature operator for the dual Weil-Petersson Teichmüller空间的全态cotangent捆绑包上的度量。
For a holomorphic vector bundle $E$ over a Hermitian manifold $M$ there are two important notions of curvature positivity, the Griffiths positivity and Nakano positivity. We study the consequence of these positivities and the relevant estimates. If $E$ is Griffiths negative over Kähler manifold, then there is a Kähler metric on its total space $E$, and we calculate the curvature and prove the non-positivity of the curvature along the tautological direction. The Nakano positivity can be formulated as a positivity for the Nakano curvature operator and we give estimate the Nakano curvature operator associated with a Nakano positive direct image bundle. As applications we construct a mapping class group invariant Kähler metric on the quasi-Fuchsian space QF$(S)$, which extends the Weil-Petersson metric on the Teichmüller space $\mathcal{T}(S)\subset {\rm QF}(S)$, and we obtain estimates for the Nakano curvature operator for the dual Weil-Petersson metric on the holomorphic cotangent bundle of Teichmüller space.
