Abstract
We show that compact Kähler manifolds have the rational cohomology ring of complex projective space provided a weighted sum of the lowest three eigenvalues of the Kähler 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 Kähler manifolds.
Acknowledgements
We would like to thank Greg Kallo for many conversations.
References
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Articles in the same Issue
- Frontmatter
- Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces
- A support theorem for\break the Hitchin fibration: The case of GLn and KC
- Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
- Quasiexcellence implies strong generation
- Serre–Tate theory for Calabi–Yau varieties
- Vanishing and estimation results for Hodge numbers
- Torus actions, maximality, and non-negative curvature
- Local-to-global Urysohn width estimates
Articles in the same Issue
- Frontmatter
- Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces
- A support theorem for\break the Hitchin fibration: The case of GLn and KC
- Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
- Quasiexcellence implies strong generation
- Serre–Tate theory for Calabi–Yau varieties
- Vanishing and estimation results for Hodge numbers
- Torus actions, maximality, and non-negative curvature
- Local-to-global Urysohn width estimates