Let us consider the pseudo-euclidean space $\mathbb{R}^3_1$; that is, the space $\mathbb{R}^3$ endowed with the metric

$$\langle x, y\rangle = x_1y_1+x_2y_2-x_3y_3.$$

I see in O'Neill's book that there does not exist any compact semi-riemannian hypersurface in this space. In fact, there does not exist any compact hypersurface in the general case $\mathbb{R}^n_\nu$ where $\nu$ is the index of the metric. Why does this kind of phenomenon occur in the pseudo-euclidean case?