Volume Growth and Curvature Decay of Complete Positively Curved Kähler Manifolds

Details Volume Growth and Curvature Decay of Complete Positively Curved Kähler Manifolds Volume Growth and Curvature Decay of Complete Positively Curved Kähler Manifolds

2008-06-09

arxiv.org/abs/0806.1325v1

Chinese Journal of Contemporary Mathematics, Vol 28, No 1, 2007, p69-76

Mathematics

Metric Geometry

Scientific paper

This paper constructs a class of complete K\"{a}hler metrics of positive holomorphic sectional curvature on ${\bf C}^n$ and finds that the constructed metrics satisfy the following properties: As the geodesic distance $\rho\to\infty,$ the volume of geodesic balls grows like $O(\rho^{\frac{2(\beta+1)n}{\beta+2}})$ and the Riemannian scalar curvature decays like $O(\rho^{-\frac{2(\beta+1)}{\beta+2}}),$ where $\beta\geq 0.$

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