I'm trying to read section 3 in J. Jost and Y.L. Xin, title = {{Bernstein type theorems for higher codimension.}}, year = {1999}, journal = {{Calculus of Variations}}, volume = {9}, pages = {277--296}. This section has to do with the geometry of Grassmannians. I have a question that comes out of the derivation at the top of page 283 in that paper. Let M be a locally symmetric Riemannian manifold. Let c be a geodesic in M and let J be a Jacobi field along c. Let cdot be the derivative (differential) of c and assume J is orthogonal to cdot. Under these hypothees is it the case that the Lie bracket, [cdot, J], is 0? If so, why?