We illustrate how the formation of energy-preserving shocks for polytropic accretion and temperature-preserving shocks for isothermal accretion are influenced by various geometrical configurations of general relativistic, axisymmetric, low angular momentum flow in the Kerr metric. Relevant pre- and post-shock states of the accreting fluid are studied. An elegant eigenvalue-based analytical method is introduced to provide qualitative descriptions of the phase orbits corresponding to stationary transonic accretion solutions without resorting to involved numerical schemes. Effort is made to understand how weakly rotating flows behave in close proximity to the event horizon and how such “quasi-terminal” behaviours are influenced by the black hole spin for different flow geometries. The utility of such low angular momentum general relativistic accretion model probing regions of strong gravity is discussed in the context of Galactic Centre shadow imaging.