  The Light Front Holographic (LFH) wave equation, which is the conformal
scalar equation on the plane, is revisited from the perspective of the
supersymmetric quantum mechanics, and attention is drawn to the fact that it
naturally emerges in the small hyperbolic angle approximation to the "curved"
Higgs oscillator on the hyperbolic plane, i.e. on the upper part of the
two-dimensional hyperboloid of two sheets, a space of constant negative
curvature. Such occurs because the particle dynamics under consideration
reduces to the one dimensional Schr\"odinger equation with the second
hyperbolic P\"oschl-Teller potential, whose flat-space (small-angle) limit
reduces to the conformally invariant inverse square distance plus harmonic
oscillator interaction, on which LFH is based. In consequence, energies and
wave functions of the LFH spectrum can be approached by the solutions of the
Higgs oscillator on the hyperbolic plane in employing its curvature and the
potential strength as fitting parameters. Also the proton electric charge form
factor is well reproduced within this scheme by means of a Fourier-Helgason
hyperbolic wave transform of the charge density. In conclusion, in the small
angle approximation, the Higgs oscillator on the hyperbolic plane is
demonstrated to satisfactory parallel essential outcomes of the Light Front
Holographic QCD. The findings are suggestive of associating the hyperboloid
curvature of the with a second scale in LFH, which then could be employed in
the definition of a chemical potential.
