Abstract
Let W-n be C-infinity complete, simply connected n-dimensional Riemannian manifolds without conjugate points. Assume that S subset of W-2 is starshaped where ker S not equal S. For every point x is an element of S\kerS, define A(x) = {y: y lies on some geodesic segment in S from x to a point of kerS}. There is a finite collection A of all maximal A sets whose union is S. Further, kerS = boolean AND{A : A in A}.