For which values of c is the topological space xc : = {(x, y) € c^2 e: x^2 - y^2 = c} a riemann surface? you do not need to explicitly construct charts, but you do need to prove your answer is correct. (warning: use the implicit function theorem to produce a complex structure. the hardest part is proving that x. is not a manifold for certain values of c. if you get stuck, try drawing a picture.)