There is no need for signs, fences, etc. to keep people out to establish trespassing. As you acknowledge, you are not a student there; you were on property belonging to the university (a campus sidewalk); and were not on public land (e.g. a public sidewalk or road). Yes, you can be arrested and charged with trespassing, because you do not, despite any public funding for the university, have a right to be on its property if it does not want you there. The university can control access to its sidewalks (or parking lots, fields, etc.) as much as it can to its buildings.