Parking motorbike for 4 months with an empty tank

It's the first time that I have to park my motorbike for a considerably long period. 4 months during the winter to be exact. (A month and a half has already passed). And I thought I should do it with an empty tank. But recently read that it should be parked with a full tank instead. What should I do in this case? Shall I bring lots of petrol somehow and tank it up? Or even a bit would suffice?

Another question I had is about the tyres? I again read that its better to keep moving the motorbike, so as not to have the same contact point for a long period. The problem is that I don't have a lot of room to keep moving the bike. Space is a huge issue here in Munich.

It's a Kawasaki Vulcan 900 classic, 2009 model.
Thanks in advance for your help.