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A Sasakian manifold is a contact manifold $(M,\theta)$ equipped with a special kind of Riemannian metric $g$, called a Sasakian metric.

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Spin structures on Sasakian manifolds and the Kähler analogy

Every Sasakian manifold $M$ (of dimension $2k+1$) has a canonical $\mathrm{Spin}^c$ structure, because the cone $\overline{M}$ over $M$ is Kähler and thus has a canonical $\mathrm{Spin}^c$ structure …
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