arXiv 0806.13252008-06-09math.MGmath.DG

Volume Growth and Curvature Decay of Complete Positively Curved Kähler Manifolds

Xiaoyong Fu, Zhenglu Jiang

发表信息：: Chinese Journal of Contemporary Mathematics, Vol 28, No 1, 2007, p69-76

英文摘要：

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

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