Free fall motion in an invariant field of forces: the 2D-case.
Frenet formulas and geodesics in Sol geometry.
Generalized timelike Mannheim curves in Minkowski space-time .
Generic properties of closed geodesics on smooth hypersurfaces.
Geodesic conjugation of two-step nilmanifolds. (Conjugaison géodésique des nilvariétés de rang deux.)
Geodesic graphs in Randers g.o. spaces
The concept of geodesic graph is generalized from Riemannian geometry to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined and geodesic graphs in these Finsler g.o. manifolds are constructed. New structures of geodesic graphs are observed.
Geodesic knots in the figure-eight knot complement.
Geodesic laminations with transverse Hölder distributions
Geodesic monotone vector fields.
Geodesic reduction via frame bundle geometry.
Geodesic spheres and isometric flows
Geodesically complete Lorentzian metrics on some homogeneous 3 manifolds.
Geodesically equivalent metrics on homogenous spaces
Two metrics on a manifold are geodesically equivalent if the sets of their unparameterized geodesics coincide. We show that if two -invariant metrics of arbitrary signature on homogenous space are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that the existence of nonproportional, geodesically equivalent, -invariant metrics on homogenous space implies that their holonomy algebra cannot be full. We give an algorithm for...
Geodesics and deformed pseudo-Riemannian manifolds with symmetry.
Geodesics and Totally Convex Sets on Surfaces.
Geodesics in Asymmetic Metric Spaces
In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”). In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local) compactness.We define the geodesics using as admissible paths the class of run-continuous paths.We...
Geodesics in the Heisenberg Group
We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from the center of the group.
Geodesics on a central symmetric warped product manifold.
Geodesics on Lorentzian manifolds with quasi-convex boundary.
Geodesics on non static Lorentz manifolds of Reissner-Norström type.