The Jacobi map
Using two-parameter variations of a geodesic in a semi-Riemannian manifold, the author introduces \(n\)-th order Jacobi vector fields. He obtains necessary and sufficient conditions for an \(n\)-th order Jacobi field to be the variation vector field as well as the index theorem, giving upper and lower bounds for the focal multiplicity.
scientific article; zbMATH DE number 936182