Abstract
Abstract
In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric
$\omega $
such that
$(T_X,\omega )$
is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then there exists a uniformly RC-positive complex Finsler metric on
$T_X$
.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Cited by
4 articles.
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1. On Almost Nonpositive k-Ricci Curvature;The Journal of Geometric Analysis;2022-09-23
2. Kähler manifolds and mixed curvature;Transactions of the American Mathematical Society;2022-08-24
3. On projective manifolds with semi-positive holomorphic sectional curvature;American Journal of Mathematics;2022-06
4. The fundamental group, rational connectedness and the positivity of Kähler manifolds;Journal für die reine und angewandte Mathematik (Crelles Journal);2020-12-16