Hermitian metrics of negative holomorphic sectional curvature on some hyperbolic manifolds

Cheung, Chi-Keung

doi:10.1007/bf01161998

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…Let us close this section by extending an old result of Cheung [10]: Theorem 3.15. Let (M 2 , ω) be a Kähler-Einstein surface with Ric ω = λω.…”

Section: (I) If Ricmentioning

confidence: 58%

On the weighted orthogonal Ricci curvature

Broder¹,

Tang²

2021

Preprint

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We introduce the weighted orthogonal Ricci curvature -a two-parameter version of Ni-Zheng's orthogonal Ricci curvature. This curvature serves as a very natural object in the study of the relationship between the Ricci curvature(s) and the holomorphic sectional curvature. In particular, in determining optimal curvature constraints for a compact Kähler manifold to be projective. In this direction, we prove a number of vanishing theorems using the weighted orthogonal Ricci curvature(s) in both the Kähler and Hermitian category.

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“…Let us close this section by extending an old result of Cheung [10]: Theorem 3.15. Let (M 2 , ω) be a Kähler-Einstein surface with Ric ω = λω.…”

Section: (I) If Ricmentioning

confidence: 58%

On the weighted orthogonal Ricci curvature

Broder¹,

Tang²

2021

Preprint

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“…In particular, people have been interested in knowing whether X admits a metric of negative curvature in an appropriate sense. Interesting results in this direction include the work of Tsai [11], who constructed a Hermitian metric of negative holomorphic bisectional curvature on a Kodaira surface, and the work of Cheung [4], who showed that there exists a Kähler metric of negative holomorphic sectional curvature on any Kodaira surface. It remains an open question whether any Kodaira surface admits a Kähler metric of negative holomorphic bisectional curvature.…”

Section: Introductionmentioning

confidence: 99%

Kähler metrics of negative holomorphic bisectional curvature on Kodaira surfaces

Yeung²

2011

Bulletin of the London Mathematical Society

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Hermitian metrics of positive holomorphic sectional curvature on fibrations

Chaturvedi

Heier

2019

Math. Z.

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The main result of this note essentially is that if the base and fibers of a compact fibration carry Hermitian metrics of positive holomorphic sectional curvature, then so does the total space of the fibration. The proof is based on the use of a warped product metric as in the work by Cheung in case of negative holomorphic sectional curvature, but differs in certain key aspects, e.g., in that it does not use the subadditivity property for holomorphic sectional curvature due to Grauert-Reckziegel and Wu.

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Hermitian metrics of negative holomorphic sectional curvature on some hyperbolic manifolds

Cited by 7 publications

References 14 publications

On the weighted orthogonal Ricci curvature

On the weighted orthogonal Ricci curvature

Kähler metrics of negative holomorphic bisectional curvature on Kodaira surfaces

Hermitian metrics of positive holomorphic sectional curvature on fibrations

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