A Morse index theorem for geodesics on a glued Riemannian space (Q1772508)

A glued Riemannian space is obtained from Riemannian manifolds \(M_1\) and \(M_2\), by identifyng some isometric submanifolds \(B_1\) and \(B_2\). (In general, it is not a smooth Riemannian manifold, and equality of dimensions is not required.) A \(B\)-geodesic in a glued Riemannian space is a geodesic on \(M_1\) and \(M_2\) respectively, such that it has the same projected velocity in \(TB_1=TB_2\), and assume the same value on the respective metric tensors at its points in \(B_1=B_2\). The notion of Jacobi fields, conjugated points, and Morse index are studied for these \(B\)-geodesics.