  Gapless fracton phases are characterized by the conservation of certain
charges and their higher moments. These charges generically couple to higher
rank gauge fields. In this paper we study systems conserving charge and dipole
moment, and construct the corresponding gauge fields propagating in arbitrary
curved backgrounds. The relation between the symmetries of these class of
systems and spacetime transformations is discussed. In fact, we argue that
higher rank symmetric gauge theories are closer to gravitational fields than to
a standard gauge theory.
