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I'm studying General Relativity and Differential Geometry. In my text book, the author has written ##x^2=d(x,.)## where d(x,y) is distance between two points ##x,y\in M##. I couldn't understand what d(x,.) means. Moreover, I am not sure if this is generally true to write ##x^2=g_{\mu\nu} x^\mu x^\nu=d(x,.)##. Under what conditions can one write ##x^2=d(x,.)##?