  The fluid-gravity correspondence documents a precise mathematical map between
a class of dynamical spacetime solutions of the Einstein field equations of
gravity and the dynamics of its corresponding dual fluid flows governed by the
Navier-Stokes (NS) equations of hydrodynamics. This striking connection has
been explored in several dynamics-based approaches and has surfaced in various
forms over the past four decades. In a recent construction, it has been shown
that the manifold properties of geometric duals are in fact intimately
connected to the dynamics of incompressible fluids, thus bypassing the
conventional on-shell standpoints. Following such a prescription, we construct
the geometrical description that effectively captures the dynamics of an
incompressible NS fluid with respect to a uniformly rotating frame. We propose
the gravitational dual(s) described by bulk metric(s) in $(p+2)$-dimensions
such that the equations of parallel transport of an appropriately defined bulk
velocity vector field when projected onto an induced timelike hypersurface
require that the incompressible NS equation of a fluid relative to a uniformly
rotating frame be satisfied at the relevant perturbative order in
$(p+1)$-dimensions. We argue that free fluid flows on manifold(s) described by
the proposed metric(s) can be effectively considered as an equivalent theory of
non-relativistic viscous fluid dynamics with respect to (w.r.t) a uniform
rotating frame. We also present suggestive insights as to how space-time
rotation parameters encode information pertaining to the inertial effects in
the corresponding fluid dual.
