Consider a 2-dimensional surface with (r1,a2) = (0,ø) (the usual spherical polar angles) and metric ds2 rdo2? sin20 dd2, where ro> 0 is a constant. you are given that the only non-zero christoffel symbols are гу — га 2 2 1 cot 0 cos 0 г. - sin 12 21 22 (a) prove that if a contravariant vector a' undergoes parallel transport around the circle -п/4 from ф %—o to ф%3d 2т аnd a' — 0, a? 3d 1 at ф 3 0, then at ф — 2т we have acos(2t) sin(27) 2 a (b) show that the components ri1, r22 of the ricci tensor are r11 1 r22 -sin20 find r, the ricci scalar