Levi-Civita Ricci-flat metrics on non-K\"{a}hler Calabi-Yau manifolds
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Publication:6396162
DOI10.1007/S12220-022-01114-8arXiv2204.04824MaRDI QIDQ6396162
Publication date: 10 April 2022
Abstract: In this paper, we provide new examples of Levi-Civita Ricci-flat Hermitian metrics on certain compact non-K"{a}hler Calabi-Yau manifolds, including every compact Hermitian Weyl-Einstein manifold, every compact locally conformal hyperK"{a}hler 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.
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Local differential geometry of Hermitian and Kählerian structures (53B35) Conformal structures on manifolds (53C18) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)
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