By the technique of length-decreasing variations, we mean a method used by Synge, Morse, Frankel, and many others. The method consists of showing that certain minimization problems in the theory of geodesics in the large, frequently associated with topological questions, cannot have a nontrivial solution by proving that any extremal for the problem has a variation into nearby curves of strictly smaller length. Thus, Synge [8] shows that an even-dimensional orientable compact manifold of positive sectional curvatures must be simply-connected. Frankel [2], [3] shows that two compact minimal hypersurfaces in a manifold of positive Ricci curvatures must intersect. Morse [6] studies e.g. critical chords of submanifolds of Euclidean space. In Part I, we study hypersurfaces in manifolds of positive Ricci curvatures. Frankel [3] has shown that the fundamental groups of such manifolds are homomorphs of the fundamental groups of their minimal hypersurfaces. We reprove this theorem by a slightly different method from that used by Frankel and generalize it by allowing the hypersurfaces to be not necessarily minimal. If suitable curvature hypotheses are satisfied, the fundamental group of the manifold is a homomorph of the fundamental group of a certain component of the complement of the hypersurface. A precise statement of the result is given as Theorem 1. Klingenberg has proved that under various hypotheses on the sectional curvatures, connectivity, and dimension of a manifold, its injectivity radii are >7r (cf. [5]). In Part II, we introduce the of an embedded hypersurface, dual to the injectivity radius of a point, and show in Theorem 2 that, in a manifold of positive sectional curvatures bounded above by 1, the thickness of a separating totally geodesic hypersurface is ?_r/2. In case a separating hypersurface is not totally geodesic, we show in Theorem 3 that, in one of the components of its complement, it may have a collar neighborhood whose thickness can be explicitly estimated. All manifolds will be smooth with a complete Riemannian metric. M will be a manifold of dimension n with a smoothly embedded hypersurface N. Let the metric on M be denoted by (., ) and the asso-