Conjugate points on a limiting extremal
AUTOR(ES)
Morse, Marston
RESUMO
Theorem 1, together with the author's extensions of the Sturmian Comparison Theorems, will suffice to establish the basic Theorem 27.3, p. 211 of Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. Mathematical Notes, Princeton University Press, Princeton, N.J., 1976. Here and in the preceding reference there is given a Weierstrass Integral on a compact, connected, Riemannian manifold Mn, conditioned as in the above reference. Let γ be an arbitrary extremal of J joining a point P to a point Q, ≠ P on Mn. An extremal ζ of J joining A to B is termed nondegenerate if A and B are not conjugate on ζ. The index of ζ is by definition the “count” of conjugate points of A on ζ definitely preceding B.
