proper use of 'that' demonstrative

I'm confused about how to use the 'that' demonstrative in the following sentence:

Finally, in Part 4 we analysed the results that obtained in the parts mentioned above, and we showed further experiments we have done to contribute to the topics of those parts.

In the first bold clause, I used that because results is defined in the context before. And in the second bold clause, I didn't use that after the word experiments because further experiments were not defined.

Is this correct?

Solution 1:

Obtained has a slightly different meaning with and without an object. From Lexico:

VERB

1 [with object] Get, acquire, or secure (something)

‘adequate insurance cover is difficult to obtain’

2 formal [no object] Be prevalent, customary, or established.

‘the price of silver fell to that obtaining elsewhere in the ancient world’

In the sentence as written that introduces a relative clause where the understood stubject is results and the definition of obtain would be number 2 from above.

If you wanted to use obtain with definition 1 from above, you'd have to change your sentence so that obtained is in the passive:

...the results obtained...

...the results that were obtained...