  We present a formulation of the generalised uncertainty principle based on
commutator $\left[ {\hat x}^i, {\hat p}_j \right]$ between position and
momentum operators defined in a covariant manner using normal coordinates. We
show how any such commutator can acquire corrections if the momentum space is
curved. The correction is completely determined by the extrinsic curvature of
the surface $p^2=$ constant in the momentum space, and results in
non-commutativity of normal position coordinates $\left[ {\hat x}^i, {\hat x}^j
\right] \neq 0$. We then provide a construction for the momentum space geometry
as a suitable four dimensional extension of a geometry conformal to the three
dimensional relativistic velocity space - the Lobachevsky space - whose
curvature is determined by the dispersion relation $F(p^2)=-m^2$, with $F(x)=x$
yielding the standard Heisenberg algebra.
