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Manifolds with positive orthogonal Ricci curvature
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 143, Number 3, June 2021
- pp. 833-857
- 10.1353/ajm.2021.0021
- Article
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abstract:
In this paper we study the class of compact K\"ahler manifolds with ${\rm Ric}^\perp>0$. First we illustrate examples of K\"ahler manifolds with ${\rm Ric}^\perp>0$ on K\"ahler C-spaces, and construct ones on certain projectivized vector bundles. These examples show the abundance of K\"ahler manifolds which admit metrics of ${\rm Ric}^\perp>0$. Secondly we prove some (algebraic) geometric consequences of the condition ${\rm Ric}^\perp>0$ to illustrate that the condition is also quite restrictive. Finally this last point is made evident with a classification result in dimension three and a partial classification in dimension four.