Deformation of Sasakian metrics

Details Deformation of Sasakian metrics Deformation of Sasakian metrics

2008-09-26

arxiv.org/abs/0809.4699v5

Mathematics

Differential Geometry

35 pages, mistakes in lines 37--41 of page 12 of the previous version were corrected, a general revise was done to make the ma

Scientific paper

Deformations of the Reeb flow of a Sasakian manifold as transversely K\"ahler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as transversely holomorphic Riemannian flows. We also prove a Kodaira-Akizuki-Nakano type vanishing theorem for basic Dolbeault cohomology of homologically orientable transversely K\"ahler foliations. As a consequence of these results, we show that any small deformations of the Reeb flow of a positive Sasakian manifold admit compatible Sasakian metrics.

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