Observer-invariant time derivatives on moving surfaces

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