Question 2. Hyperbolic metrics (30 marks) Consider the upper half plane H2 = {(x, y) E R2\y >0} with the hyperbolic metric g= }(da? + dy?). yu 1. Show that all geodesics on the hyperbolic plane H are the circles and lines that orthogonal to the hyperplane y = 0. 2. Show that H is complete. (Hint: As question 2 in Tutorial 9, it suffices to show that the length of geodesic starting from any point po = (x(0), y(0)) E H is infinite.) 3. Find the sectional curvatures and the Riemannian curvature tensor. Question 2. Hyperbolic metrics (30 marks) Consider the upper half plane H2 = {(x, y) E R2\y >0} with the hyperbolic metric g= }(da? + dy?). yu 1. Show that all geodesics on the hyperbolic plane H are the circles and lines that orthogonal to the hyperplane y = 0. 2. Show that H is complete. (Hint: As question 2 in Tutorial 9, it suffices to show that the length of geodesic starting from any point po = (x(0), y(0)) E H is infinite.) 3. Find the sectional curvatures and the Riemannian curvature tensor