  We investigate the finite-size scaling of the boundary quantum geometric
tensor (QGT) numerically close to the Anderson localization transition in the
presence of small external magnetic fields. The QGT exhibits universal scaling
and reveals the crossover between the orthogonal and unitary critical states in
weak random magnetic fields. The flow of the QGT near the critical points
determines the critical exponents. Critical distributions of the QGT are
universal and exhibit a remarkable isotropy even in a homogeneous magnetic
field. We predict universal and isotropic Hall conductance fluctuations at the
metal-insulator transition in an external magnetic field.
