06 janeiro 2010
The Jacobi vector fields along a geodesic passing through a point p of an n-dimensional manifold M form a 2n dimensional vector space. One of the vector fields is gamma, tangent to the geodesic; another is t times gamma, where t is a distance function. The remaining Jacobi fields are the ones that determine the existence of conjugate points. Physicists tend to ignore t gamma completely; in a mathematician's scroll it may be mentioned once and then ignored, like Queen Vashti. But it is much loved by engineers, who give it the affectionate nickname "x" because in coordinates t gamma = x = x^i d/dx^i. Should we call it the polytechnique vector?