Morse index theorem
= Morse index theorem
{c}
{title2=$\operatorname{ind}(\gamma)=\sum_{0<t<1}\operatorname{mult}(t)$}
The <Morse index> of a fixed-endpoint <geodesic> equals the number of <conjugate points> strictly between its endpoints, counted with multiplicity. Its nullity equals the multiplicity of the terminal conjugate point. A conjugate multiplicity is the dimension of the space of <Jacobi fields> vanishing at the initial point and at the point in question.