While thinking about probability theory and probability distributions, I realized that I could name several multivariate distributions but could not name any multivariate distributions of genus $g=0.$ It could be that I don't know enough multivariate distributions, but it seems to me that distributions with $g=0$ are quite uncommon if not rare. What I mean by genus $0$ is that the topology of the shape of the distribution is sphere-like, (a sphere has genus $0$).
Can anyone give me an example of a multivariate pdf with genus $0$?
Integrating over the enclosed volume of the distribution would give the total proability i.e. $1.$