Following the steps suggested in this answer, I managed to set a repository on my local machine, push it to the bare repository on the dropbox folder and clone it to another local location. That is, invoked git clone ~/Dropbox/git/project.git . in a directory ~/project-image. This means that it seem to work fine - at least for me alone.
However, I don't manage to clone it using https. From dropbox I obtained the URL of ~/Dropbox/git/project.git and then tried something like
git clone https://www.dropbox.com/sh/xxxxxxx/xxxxxxx .
in another directory ~/project/image2~. This didn't work... I got the following error:
warning: remote HEAD refers to nonexistent ref, unable to checkout.
In the answer I mentioned it seems like it is possible to share the bare repository from dropbox. How? It seems like the URL of the subdirectories changes for each subdirectory and thus git cannot clone. Is this the reason? Is there a way to overcome this? Note that I don't want to put the repository on the public part of my dropbox and I want to share a link if needed.
Edit - Verify the repository on dropbox: As per @Idx suggestion I ran, in ~/Dropbox/git the following: cat project.git/HEAD which returned ref: refs/heads/master.