On 3-dimensional asymptotically harmonic manifolds

On 3-dimensional Asymptotically Harmonic Manifolds

Let (M, g) be a complete, simply connected Riemannian manifold of dimension 3 without conjugate points. We show thatM is a hyperbolic manifold of constant sectional curvature −h 2 4 , provided M is asymptotically harmonic of constant h > 0.

Harmonic Morphisms with One-dimensional Fibres on Einstein Manifolds

We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Asymptotically-optimal Path Planning on Manifolds

This paper presents an approach for optimal path planning on implicitly-defined configuration spaces such as those arising, for instance, when manipulating an object with two arms or with a multifingered hand. In this kind of situations, the kinematic and contact constraints induce configuration spaces that are manifolds embedded in higher dimensional ambient spaces. Existing sampling-based app...

Efficient asymptotically-optimal path planning on manifolds

This paper presents an efficient approach for asymptotically-optimal path planning on implicitly-defined configuration spaces. Recently, several asymptotically-optimal path planners have been introduced, but they typically exhibit slow convergence rates. Moreover, these planners can not operate on the configuration spaces that appear in the presence of kinematic or contact constraints, such as ...