Deformation of Sasakian metrics
Abstract
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.
Keywords
Cite
@article{arxiv.0809.4699,
title = {Deformation of Sasakian metrics},
author = {Hiraku Nozawa},
journal= {arXiv preprint arXiv:0809.4699},
year = {2011}
}
Comments
35 pages, mistakes in lines 37--41 of page 12 of the previous version were corrected, a general revise was done to make the manuscript essentially self-contained