Observer-invariant time derivatives on moving surfaces

Observer-invariance is regarded as a minimum requirement for an appropriate definition and derived systematically from a spacetime setting, where observer-invariance is a special case of a covariance principle and covered by Ricci-calculus. The analysis is considered for tangential n-tensor fields on moving surfaces and provides formulations which are applicable for computations. For various special cases, e.g., vector fields (n = 1) and symmetric and trace-less tensor fields (n = 2) we compare material and convected derivatives and demonstrate the different underlying physics.