Editor tracking is not working on my geometric network feature classes.
Although I enabled the editor tracking - dates and times are not recorded in layers while editing.
Is it impossible? or a local problem with my geodatabase?
There is no relevance between geometric network and editor tracking; they are two separate things. The snapshot you have shared indicates that you have enabled editor tracking with this feature class. If you can't see the dates fields, you may have hide them. So remove the layer and then re add it to the map and check whether the problem is solved!