Thanks for reading my question. I'm wonder why a symplectic form should be closed. I found many different answers in the internet, but it sounds like a technical requirement (if we omit this requisit, we obtain almost symplectic structures, insteresting as well). Why do yo think? I just want to have a fresh perspective. Thank you in advance.
There are many reasons why we might want a symplectic form to be closed by definition. Here are a few:
There's other reasons based on physical considerations as well. In short, closedness of a symplectic form is a rather mild condition that gives rise to a lot of nice structure we wouldn't otherwise have.