A note on the differential of the exponential map and Jacobi fields in a symmetric space (Q801308)

The author states a relationship between the differential of the exponential map and Jacobi fields, in a manifold M with a torsion-free affine connection. If M is an affine symmetric space, an explicit form of a Jacobi field is also given. From these results, the author obtains two well known formulas on the differential of the exponential map, in a symmetric space and in a Lie group [\textit{S. Helgason}, Differential geometry, Lie groups and symmetric spaces (1978; Zbl 0451.53038)]