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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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Accepted
$S^3$ as a Sasakian Manifold
I will answer your question for $S^{2n+1}$, since there is no difference between the case $n=1$ and the case of general $n$.
Let $(M^{2n+1},g,\theta)$ be a Sasakian manifold. One definition of a Sas …