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Deformation of Sasakian metrics

Authors
  • Nozawa, Hiraku
Type
Preprint
Publication Date
Oct 07, 2011
Submission Date
Sep 26, 2008
Identifiers
arXiv ID: 0809.4699
Source
arXiv
License
Yellow
External links

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.

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