Product variables

How can I get out priduct category/subcategories variable.
For example to get product name there is such line: By what should I replace product_name to get all product parent categoryes?

Parent categories are not loaded from the database on the product page. That means that you can't just use $this->element->something.
You need to first do a query in MySQL in order to load the categories data from the database and then you can use the data your loaded to display it.