A Euclidean-like space having line element d s^2 = (d z^1)^2 + ... + (d z^p)^2 - (d z^(p + 1))^2 - ... - (d z^(p + q))^2, having dimension m = p + q. In contrast, the signs would be all be positive for a Euclidean space.

Campbell's theorem | Euclidean space

Euclid