  Observer-invariance is regarded as a minimum requirement for an appropriate
definition of time derivatives. We systematically discuss such time derivatives
for surface tensor field and provide explicit formulations for material,
upper-convected, lower-convected and Jaumann/corotational time derivatives
which all lead to different physical implications. We compare these results
with the corresponding time derivatives for tangential tensor fields. As
specific surface 2-tensor fields we consider surface Q-tensor fields and
conforming surface Q-tensor fields and apply the results in surface Landau-de
Gennes models for surface liquid crystals.
