2.10. Consider the vector field X(x1, x2) = (x1, x2, 1, 0) on R?. For te R and pe R?, let o.(p) = a,(t) where a, is the maximal integral curve of X through p. (a) Show that, for each t, q, is a one to...

Differential Geometry. Please explain as much as you can

Extracted text: 2.10. Consider the vector field X(x1, x2) = (x1, x2, 1, 0) on R?. For te R and pe R?, let o.(p) = a,(t) where a, is the maximal integral curve of X through p. (a) Show that, for each t, q, is a one to one transformation from R? onto itself. Geometrically, what does this transformation do? (b) Show that Po = identity Pin +t2 = Pt, ° P12 for all t1, t2 e R %3D P-1 = P for all t e R. [Thus t-o, is a homomorphism from the additive group of real numbers into the group of one to one transformations of the plane.]