RC-positive metrics on rationally connected manifolds
Xiaokui Yang
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 $T_X$ .
Topics & Concepts
Metric (unit)Manifold (fluid mechanics)MathematicsProjective testPure mathematicsOmegaHermitian manifoldTopology (electrical circuits)CombinatoricsPhysicsGeometryRicci curvatureQuantum mechanicsEngineeringOperations managementMechanical engineeringEconomicsCurvatureAdvanced Differential Geometry ResearchGeometry and complex manifoldsGeometric Analysis and Curvature Flows