Deformation of Sasakian metrics

Hiraku Nozawa

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arXiv · 0809.4699

Deformation of Sasakian metrics

Hiraku Nozawa

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Abstract

Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler 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 Kähler 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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Hiraku Nozawa. 2011-10-07. Deformation of Sasakian metrics. https://arxiv.org/abs/0809.4699

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