  In this paper, we show how the restriction of the Quantum Geometric Tensor to
manifolds of states that can be generated through local interactions provides a
new tool to understand the consequences of locality in physics. After a review
of a first result in this context, consisting in a geometric out-of-equilibrium
extension of the quantum phase transitions, we argue the opportunity and the
usefulness to exploit the Quantum Geometric Tensor to geometrize quantum chaos
and complexity.
