I am reading the Wikipedia page on Sasakian manifolds, which has the following definition:
A Sasakian metric is defined using the construction of the ''Riemannian cone''. Given a Riemannian manifold $(M,g)$, its Riemannian cone is a product
$$(M\times {\Bbb R}^{>0})$$
of $M$ with a half-line ${\Bbb R}^{>0}$, equipped with the ''cone metric''
$$t^2 g + dt^2,$$
where $t$ is the parameter in ${\Bbb R}^{>0}$.
A manifold $M$ equipped with a 1-form $\theta$ is contact if and only if the 2-form
$$t^2\,d\theta + 2t\, dt \cdot \theta$$
on its cone is symplectic (this is one of the possible definitions of a contact structure). A contact Riemannian manifold is Sasakian, if its Riemannian cone with the cone metric is a Kähler manifold with Kähler form
$$t^2\,d\theta + 2t\,dt \cdot \theta.$$
What does it mean to take the dot product $\cdot$ of the one-forms $2t\,dt$ and $\theta$, to somehow get a two-form? Or is this a typo or variant notation for the wedge / exterior product $\wedge$?
I don't think this is supposed to depend on the metric $g$.