Jacobi vector fields along geodesics in glued Riemannian manifolds (Q699974)

A glued Riemannian manifold \(M\) is a union of complete connected Riemannian manifolds which are glued at their boundaries. Some examples of surfaces of cylinders, surfaces of cones, tubular hypersurfaces are constructed. The variation vector fields along geodesics (locally minimizing curves) on \(M\) satisfy the Jacobi equation in each component manifold. This paper gives the equation showing how Jacobi vector fields change when passing across the boundary of a component manifold into the neighboring component and obtains a criterion characterising glueing boundaries separating conjugate points.