Vanishing and estimation results for Hodge numbers

Peter Petersen, Matthias Wink

Type: Article

Publication Date: 2021-08-07

Citations: 2

DOI: https://doi.org/10.1515/crelle-2021-0036

Abstract

We show that compact K\"ahler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the K\"ahler curvature operator is positive. This follows from a more general vanishing and estimation theorem for the individual Hodge numbers. We also prove an analogue of Tachibana's theorem for K\"ahler manifolds.

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arXiv (Cornell University) - View - PDF
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Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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Works Cited by This (30)

Action	Title	Year	Authors
+ PDF Chat	The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature	1988	Ngaiming Mok
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+ PDF Chat	A Note on Kahler-Ricci Soliton	2009	Xiao Chen Song Sun Gang Tian
+	Projective Manifolds with Ample Tangent Bundles	1979	Шигефуми Мори
+ PDF Chat	Vector fields and Ricci curvature	1946	S. Bochner
+ PDF Chat	Einstein manifolds with nonnegative isotropic curvature are locally symmetric	2009	Simon Brendle
+ PDF Chat	On Kähler manifolds with positive orthogonal bisectional curvature	2007	X.X. Chen
+	Riemannian spaces with exceptional holonomy groups	1968	D. V. Alekseevskiĭ
+ PDF Chat	A new proof of Mok’s generalized Frankel conjecture theorem	2008	Hui-Ling Gu
+	On holomorphic sections of certain hermitian vector bundles	1970	Shôshichi Kobayashi Hung-Hsi Wu