What is the metallic character of carbon?
Carbon can have positive oxidation states, and in the form of graphite carbon can conduct electricity.
One characteristic of metals is that metals form positive oxidation states when forming bonds with other elements. Metals generally have low electronegativities and so tend to share electrons such that the electron density is away from the metallic nucleus.
Carbon, especially, when it bonds with oxygen to form polyatomic ions, has a positive partial charge and the electrons from carbon tend to have a greater density nearer the oxygen nucleus. This is a metallic character of carbon.
Another characteristic of metals is that they conduct electricity. Carbon in the form of graphite can conduct electricity. This is a metallic character of carbon.