The quantum potential based on the G-dynamics of quantum covariant Hamiltonian system

Inspired by the geomentum operator and the G-dynamics of quantum covariant

Hamiltonian system (QCHS) defined by the quantum covariant Poisson bracket (QCPB) theory, we reconsider the quantum potential as part of the Schr\"{o}dinger equation by using the generalized gradient operator, and then it naturally leads to the geometric potential only associated with the scalar function as a environment variable, we present the geometric quantum potential as an extension of the quantum potential, it naturally includes the imaginary geomenergy as a part of it, meanwhile, we can deduce the quantum potential by using the imaginary geomenergy in a given condition.