  Higher dimensional theories, wherein our four dimensional universe is
immersed into a bulk ambient, have received much attention recently, and the
direction of investigation had, as far as we can discern, all followed the
ordinary Euclidean hypersurface theory's isometric immersion recipe, with the
spacetime metric being induced by an ambient parent. We note in this paper that
the indefinite signature of the Lorentzian metric perhaps hints at the lesser
known equiaffine hypersurface theory as being a possibly more natural, i.e.,
less customized beyond minimal mathematical formalism, description of our
universe's extrinsic geometry. In this alternative, the ambient is deprived of
a metric, and the spacetime metric becomes conformal to the second fundamental
form of the ordinary theory, therefore is automatically indefinite for
hyperbolic shapes. Herein, we advocate investigations in this direction by
identifying some potential physical benefits to enlisting the help of
equiaffine differential geometry.
