An exercise in Do Carmo's riemannian geometry after chapter11 'the morse index theorem'.

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Let me put the picture of this exercise below: enter image description here

Exercise 2 mentioned in the hint is the following: enter image description here My question is that in the hint, in order to show K=1 one must prove that the multiplicity of the conjugate point q in each geodesic from p is all n-1, but I don't know how to prove that. It seems only clear to me in 2 dimensional case. Any help will be appreciated.