On the Index Theorem
Leif-Norman Patterson · American Journal of Mathematics · 1963
Abstract : This paper purports to present an account of the general index problem in Riemannian geometry from a geometric point of view, to point out some of the most important index theorems, and to study some continuity questions related to the index problem. The results obtained are: 1. All self-adjoint boundary-value problems arising in Riemannian geometry can be interpreted geometrically in terms of separate endmanifolds. 2. The subsequent extension of an index theorem of Ambrose to all such problems, in particular to that associated with periodic geodesies. 3. The continuous dependence (with some exceptions) of the Ambrose conjugate points on the boundary conditions and on the Riemannian metric on the manifold.