Why no virtual ground in schmitt trigger?
In the inverting amplifier the feedback from input to output is negative, which stabilizes the output (to make the - input the same level as the + input).

In the schmitt-trigger there is positive feedback, hence the output is driven to the extreme (in the absense of supply voltage limitations, to + or - infinte). 

The 'virtual ground' concept applies onl;y when the opamp drives itself to stability (both inputs at the same level). The S.T. does exactly the opposite: it drives itself to on eof the extremes.