Generalized Covariant Derivative with Respect to Time in Flat Space (I): Eulerian Description

This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included: (a) the restricted covariant derivative with respect to time for Eulerian component is defined; (b) the postulate of the covariant form invariability in time field is set up; (c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined; (d) the algebraic structure of the generalized covariant derivative with respect to time is made clear; (e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.