Mahmut S....the 1/gm "resistance" is - in fact - no resistancenot a real resistor. And inIn no case it is a quantity which exist in a real fet and could be found between G and S. It's a pure mathematical trick to make the model to obey the same equations as the other models.
It does NOT follow ohms law because it isIn small signal AC analyses T-model works as well as the other shown models, but having a "transresistance". Its purposeresistor between G and S is confusing and makes difficult to modelsee the transconductancebasic idea of gm which represents- the control function between Vgs and Id. As a teacher of engineering students I do not like this kind of representation because it is really confusing (as we can see with your contribution), no matter it's mathematically right.
My recommendation: DontDon't use the T-model and better use. Use the equivalent models with gm as a voltage-controlled current source.