  We discuss a particular non-relativistic limit of NS-NS gravity that can be
taken at the level of the action and equations of motion, without imposing any
geometric constraints by hand. This relies on the fact that terms that diverge
in the limit and that come from the Vielbein in the Einstein-Hilbert term and
from the kinetic term of the Kalb-Ramond two-form field cancel against each
other. This cancelling of divergences is the target space analogue of a similar
cancellation that takes place at the level of the string sigma model between
the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino
term. The limit of the equations of motion leads to one equation more than the
limit of the action, due to the emergence of a local target space scale
invariance in the limit. Some of the equations of motion can be solved by scale
invariant geometric constraints. These constraints define a so-called
Dilatation invariant String Newton-Cartan geometry.
