Gaussian distribution with condition?
$$\mathcal{N}(x|m,\Sigma)=(2\pi)^{-k/2}|\Sigma|^{-1/2}\exp\left(-2^{-1}(x-m)^T\Sigma^{-1}(x-m)\right)$$
where $x,m$ are vectors of dimension $k$, $\Sigma$ is a $k\times k$ matrix, $|\Sigma|$ is its determinant. The vector $m$ represents the mean of the multivariate normal, and $\Sigma$ the covariance matrix, which must be positive definite.