  The Iwasawa manifold is uplifted to seven-folds of either G_2 holonomy or
SU(3) structure, explicit new metrics for the same having been constructed in
this work. We uplift the Iwasawa manifold to a G_2 manifold through "size"
deformation (of the Iwasawa metric), via Hitchin's Flow equations, showing also
the impossibility of the uplift for "shape" and "size" deformations (of the
Iwasawa metric). Using results of [1], we also uplift the Iwasawa manifold to a
7-fold with SU(3) structure through "size" and "shape" deformations via
generalisation of Hitchin's Flow equations. For seven-folds with
SU(3)-structure, the result could be interpreted as M5-branes wrapping
two-cycles embedded in the seven-fold - a warped product of either a special
hermitian six-fold or a balanced six-fold with the unit interval. There can be
no uplift to seven-folds of SU(3) structure involving non-trivial "size" and
"shape" deformations (of the Iwasawa metric) retaining the "standard complex
structure" - the uplift generically makes one move in the space of almost
complex structures such that one is neither at the standard complex structure
point nor at the "edge". Using the results of [2] we show that given two "shape
deformation" functions, and the dilaton, one can construct a Riemann surface
obtained via Weierstrass representation for the conformal immersion of a
surface in R^l, for a suitable l, with the condition of having conformal
immersion being a quadric in CP^{l-1}.
