A glued Riemannian space is obtained from Riemannian manifolds
M1 and
M2 by identifying their isometric submanifolds
B1 and
B2. A curve on a glued Riemannian space which is a geodesic on each Riemannian manifold and satisfies certain passage law on the identified submanifold
B :=
B1 ≅
B2 is called a
B-geodesic. Considering the variational problem with respect to arclength
L of piecewise smooth curves through
B, a critical point of
L is a
B-geodesic. A
B-Jacobi field is a Jacobi field on each Riemannian manifold and satisfies certain passage condition on
B. In this paper, we extend the Morse index theorem for geodesics in Riemannian manifolds to the case of a glued Riemannian space.
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