(1) Let S = (0,0,1). For a point p H, consider the line going through p and S, and we let be the point of this line meeting with the xy-plane. This is called the hyperbolic stereographic projection. Let a : H D be the projection map. The image is called the Poincar disk. Write down the expression of the hyperbolic stereographic projection and show that it is a diffeomorphism. (Hence, a can be understood as a global change of parameter of H2.). (2) Let T-|(u, v) be the inverse of hyperbolic stereographic projection you found in part (1). Find the expression of the first fundamental form of H in terms of (u, v). (This is the first fundamental form on the Poincar disk. Please compare your answer with that of stereographic projection on S2. ) (1) Let S = (0,0,1). For a point p H, consider the line going through p and S, and we let be the point of this line meeting with the xy-plane. This is called the hyperbolic stereographic projection. Let a : H D be the projection map. The image is called the Poincar disk. Write down the expression of the hyperbolic stereographic projection and show that it is a diffeomorphism. (Hence, a can be understood as a global change of parameter of H2.). (2) Let T-|(u, v) be the inverse of hyperbolic stereographic projection you found in part (1). Find the expression of the first fundamental form of H in terms of (u, v). (This is the first fundamental form on the Poincar disk. Please compare your answer with that of stereographic projection on S2. )