  We discover the connection between the Berry curvature and the Riemann
curvature tensor in any kinematic space of minimal surfaces anchored on
spherical entangling surfaces. This new holographic principle establishes the
Riemann geometry in kinematic space of arbitrary dimensions from the holonomy
of modular Hamiltonian, which in the higher dimensions is specified by a pair
of time-like separated points as in CFT$_1$ and CFT$_2$. The Berry curvature
that we constructed also shares the same property of the Riemann curvature for
all geometry: internal symmetry; skew symmetry; first Bianchi identity. We
derive the algebra of the modular Hamiltonian and its deformation, the latter
of which can provide the maximal modular chaos to the modular scrambling modes.
The algebra also dictates the parallel transport, which leads to the Berry
curvature exactly matching to the Riemann curvature tensor. Finally, we compare
CFT$_1$ to higher dimensional CFTs and show the difference from the OPE block.
