论文标题
Levi-civita ricci-flat指标在非kählercalabi-yau歧管上
Levi-Civita Ricci-flat metrics on non-Kähler Calabi-Yau manifolds
论文作者
论文摘要
在本文中，我们提供了levi-civita ricci-flat Hermitian指标的新示例，这些指标涉及某些紧凑的非kählercalabi-yau歧管，包括每一个紧凑型赫米尔米亚人的赫米尔米亚人Weyl-einstein歧管，每个紧凑的局部紧凑型在局部整体hyperkählerler，hyperkähller的每一个悬浮液，每种悬浮液的悬浮液，每种悬浮量都被普遍散发出来，希望偶然地播出了偶然的表现。这些示例将先前的构造推广到HOPF歧管上。此外，我们还用非负第一个Chern类构建了紧凑型赫尔米利亚流形的新示例，这些遗传阶级持续严格地严格为负riemannian标态曲率。此外，我们在研究Chern-Ricci流的研究中，我们的主要结果在紧凑的Hermitian Weyl-Einstein歧管上进行了一些应用。特别是，我们描述了某些明确的有限时间崩溃的解决方案的Gromov-Hausdorff限制，这些解决方案将先前的构造推广到HOPF歧管上。
In this paper, we provide new examples of Levi-Civita Ricci-flat Hermitian metrics on certain compact non-Kähler Calabi-Yau manifolds, including every compact Hermitian Weyl-Einstein manifold, every compact locally conformal hyperKähler manifold, certain suspensions of Brieskorn manifolds, and every generalized Hopf manifold provided by suspensions of exotic spheres. These examples generalize previous constructions on Hopf manifolds. Additionally, we also construct new examples of compact Hermitian manifolds with nonnegative first Chern class that admit constant strictly negative Riemannian scalar curvature. Further, we remark some applications of our main results in the study of the Chern-Ricci flow on compact Hermitian Weyl-Einstein manifolds. In particular, we describe the Gromov-Hausdorff limit for certain explicit finite-time collapsing solutions which generalize previous constructions on Hopf manifolds.
