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 circles on real hypersurfaces of type and in a complex space form.
Geodesics and curvature of semidirect product groups
Summary: Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of examples, like the magnetic extension of a group, are then considered.
Geodesics and deformed pseudo-Riemannian manifolds with symmetry.
Geodesics and soap bubbles in surfaces.
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 compactly supported Hamiltonian diffeomorphism group.
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.
Geodesics on nonstatic Lorentz manifolds of Reissner-Nordstrom type (Erratum).
Geodesics on open surfaces containing horns
Geodesics on product lorentzian manifolds
Geodesics on quadrics and a mechanical problem of C. Neumann.
Geodesics on S2 and periodic points of annulus homeomorphisms.
Geodesics on the Ellipsoid.
Geodesics on the tangent sphere bundles over space forms.