标题： 关于正Sasakian几何 显示英文标题

标题： On Positive Sasakian Geometry

摘要： 一个流形上的Sasakian结构被称为{\it 正数}，如果其基本第一陈类可以由相对于其横截全纯CR结构的正(1,1)-形式表示。 我们证明了一个定理，该定理指出每个正的Sasakian结构都可以变形为一个度量具有正里奇曲率的Sasakian结构。 这使我们通过例子给出了Sha和Yang [SY]的一个完全独立的证明，即对于每个正整数k，$S^2\times S^3$的k重连通和可以赋予正里奇曲率的度量。 显示英文摘要

摘要： A Sasakian structure on a manifold is called {\it positive} if its basic first Chern class can be represented by a positive (1,1)-form with respect to its transverse holomorphic CR-structure. We prove a theorem that says that every positive Sasakian structure can be deformed to a Sasakian structure whose metric has positive Ricci curvature. This allows us by example to give a completely independent proof of a result of Sha and Yang [SY] that for every positive integer k the k-fold connected sum of $S^2\times S^3$ admits metrics of positive Ricci curvature.