On the generation of smooth three-dimensional rigid body motions. Abstract This paper addresses the problem of generating smooth trajectories between an initial and final position and orientation in… (More)

We construct a pair of nite piecewise Euclidean 2-complexes with non-positive curvature which are homeomorphic but whose universal covers have nonhomeomorphic ideal boundaries, settling a question… (More)

We present a theorem of Lancret for general helices in a 3-dimensional real-space-form which gives a relevant difference between hyperbolic and spherical geometries. Then we study two classical… (More)

The purpose of this chapter is to survey some recent results and state open questions concerning the rigidity of Riemannian manifolds. The starting point will be the boundary rigidity and conjugacy… (More)

We consider compact Riemannian manifolds (M,∂M, g) with boundary ∂M and metric g on which a finite group Γ acts freely. We determine the extent to which certain rigidity properties of (M,∂M, g)… (More)

Let Ω be an (n + 1)-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary M = ∂Ω. Assume that the principal curvatures of M are bounded from below by a… (More)

Let 1 → H → G → Z → 1 be an exact sequence of hyperbolic groups induced by an automorphism φ of the free group H. Let H1(⊂ H) be a finitely generated distorted subgroup of G. Then there exist N > 0… (More)

The lines of curvature on a cyclide of Dupin are circular arcs. A surface which carries two orthogonal families of circular arcs must arise as an integral surface of an overdetermined exterior… (More)

We consider the question of when an inequality between lengths of “corresponding” geodesics implies a corresponding inequality between volumes. We prove this in a number of cases for compact… (More)