# Sasakian manifold

A Sasakian manifold is a differential manifold $M$ equipped with a contact form $\theta$ (making it a contact manifold) as well as a Riemannian metric (making it a Riemannian manifold) such that the following compatibility condition is satisfied (a Riemannian metric satisfying this special condition is termed a Sasakian metric):
$t^2 d\theta + 2t dt \wedge \theta$