简介：ThepreviouspaperreportedanewderivativeintheEuleriandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedEuleriancomponentwithrespecttotime.ThispaperextendsthethoughtfromtheEuleriandescriptiontotheLagrangiandescription:onthebasisofthepostulateofcovariantforminvariabilityintimefield,wedefineanewderivativeintheLagrangiandescriptioninflatspace—thegeneralizedcovariantderivativeofgeneralizedLagrangiancomponentwithrespecttotime.Besides,thecovariantdifferentialtransformationgroupissetup.ThecovariantforminvariabilityofLagrangianspace-timeisascertained.

简介：ThispaperreportsanewderivativeintheEuleriandescriptioninflatspace-thegeneralizedcovariantderivativewithrespecttotime.Thefollowingcontentsareincluded:(a)therestrictedcovariantderivativewithrespecttotimeforEuleriancomponentisdefined;(b)thepostulateofthecovariantforminvariabilityintimefieldissetup;(c)thegeneralizedcovariantderivativewithrespecttotimeforgeneralizedEuleriancomponentisdefined;(d)thealgebraicstructureofthegeneralizedcovariantderivativewithrespecttotimeismadeclear;(e)thecovariantdifferentialtransformationgroupintimefiledisderived.TheseprogressesrevealthecovariantforminvariabilityofEulerianspaceandtime.