Mahmut S....the 1/gm "resistance" is - in fact - no resistance. And in no case it is quantity which exist between G and S.
It does NOT follow ohms law because it is a "transresistance". Its purpose is to model the transconductance gm which represents the control function between Vgs and Id. I do not like this kind of representation because it is really confusing (as we can see with your contribution).
My recommendation: Dont use the T-model and better use the equivalent models with gm as a voltage-controlled current source.