On Positive Sasakian Geometry

الأصل · EN

A Sasakian structure on a manifold is called 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 S²× S³ admits metrics of positive Ricci curvature.