... these vectors to the curve.That is, does the vector V(4) remain parallel, and do the vectors {V(1), V(2), V(3), V(4)}remain orthogonal in the sense of 8. 2?Answer If X and Y are vector fields, ... smoothness follows. ❄Example In E3, the Levi-Civita tensor coincides with the totally antisymmetric third-ordertensor œijk in Exercise Set 5. In the Exercises, we see how to use it to generalize ... bythese vectors by justifying the following facts. (a) Restricting your attention to Riemannian 4-manifolds, let A, B, and C be vectors at m, and suppose—as you may—that you have chosen an inertial...