On Positive Sasakian Geometry

Details On Positive Sasakian Geometry On Positive Sasakian Geometry

2001-04-11

arxiv.org/abs/math/0104126v1

Geometriae Dedicata 101: 93-102, 2003.

Mathematics

Differential Geometry

9 pages

Scientific paper

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.

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