A bumpy metric theorem and the Poisson relation for generic strictly convex domains.
A characterization of Gromov hyperbolicity of surfaces with variable negative curvature.
A characterization of shortest geodesics on surfaces.
A convenient setting for differential geometry and global analysis
A convenient setting for differential geometry and global analysis II
A dynamical approach to compactify the three dimensional Lorentz group.
A general comparison theorem with applications to volume estimates for submanifolds
A geometric space without conjugate points.
A lossless reduction of geodesics on supermanifolds to non-graded differential geometry
Let be a smooth supermanifold with connection and Batchelor model . From we construct a connection on the total space of the vector bundle . This reduction of is well-defined independently of the isomorphism . It erases information, but however it turns out that the natural identification of supercurves in (as maps from to ) with curves in restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for geodesics...
A Morse theory for light rays on stably causal lorentzian manifolds
A new curvature invariant and entropy of geodesic flow.
A note on geodesic mappings of pseudosymmetric Riemannian manifolds
A note on the volume of balls on Riemannian manifolds of non-negative curvature
A property on geodesic mappings of pseudo-symmetric Riemannian manifolds.
A typical convex surface contains no closed geodesic.
Abnormal sub-riemannian geodesics : Morse index and rigidity
Abnormality of trajectory in sub-Riemannian structure
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
An algorithm based on rolling to generate smooth interpolating curves on ellipsoids
We present an algorithm to generate a smooth curve interpolating a set of data on an -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...
An elementary formula for the Fenchel-Nielsen twist.
An integrable flow on a family of Hilbert Grassmannians.