  We construct operators in holographic two-dimensional conformal field theory,
which act locally in the code subspace as arbitrary bulk spacelike vector
fields. Key to the construction is an interplay between parallel transport in
the bulk spacetime and in kinematic space. We outline challenges, which arise
when the same construction is extended to timelike vector fields. We also
sketch several applications, including boundary formulations of the bulk
Riemann tensor, dreibein, and spin connection, as well as an application to
holographic complexity.
