THIS IS FOR A DIFFERENTIAL GEOMETRY COURSE. PLEASE BE AS DETAILED AS POSSIBLE IN YOUR ANSWER. THIS IS ALL OF THE INFORMATION I AM GIVEN FOR THIS PROBLEM. THANK YOU SO MUCH IN ADVANCE!!!

PLEASE ANSWER ALL PARTS (A-D)!!

3. (25 pts in total) (a) [10pts] Let N be the North Pole of a unit sphere. Let Q and P be two points on a parallel of colatitude v in such a way that meridians NQ and NP make an angle at N. Consider a unit vector v tangent to the meridian NQ at N and take the parallel transport of v along the closed curve made up by the meridian NQ, the parallel QP and the meridian PN (see the figure below). Determine the angle from v to the final position of this parallel transport of v; P (b) (5pts) Find the geodesic curvature of a parallel of colatitude y on a unit sphere; (c) [5pts] Show that on a surface of a nonzero constant Gaussian curvature the area of a geodesic polygon is determined by its interior (or exterior) angles; (d) (5pts] On a sphere of radius R find a geodesic triangle whose interior angles are each 34. What is the area of this triangle? 3. (25 pts in total) (a) [10pts] Let N be the North Pole of a unit sphere. Let Q and P be two points on a parallel of colatitude v in such a way that meridians NQ and NP make an angle at N. Consider a unit vector v tangent to the meridian NQ at N and take the parallel transport of v along the closed curve made up by the meridian NQ, the parallel QP and the meridian PN (see the figure below). Determine the angle from v to the final position of this parallel transport of v; P (b) (5pts) Find the geodesic curvature of a parallel of colatitude y on a unit sphere; (c) [5pts] Show that on a surface of a nonzero constant Gaussian curvature the area of a geodesic polygon is determined by its interior (or exterior) angles; (d) (5pts] On a sphere of radius R find a geodesic triangle whose interior angles are each 34. What is the area of this triangle