منابع مشابه
Lorentzian Geodesic Flows between Hypersurfaces in Euclidean Spaces
There are several approaches to this question. One is from the perspective of a Riemannian metric on the group of diffeomorphisms of R. If the smooth hypersurfaces Mi bound compact regions Ωi , then the group of diffeomorphisms Diff(R) acts on such regions Ωi and their boundaries. Then, if φt, 1 ≤ t ≤ 1, is a geodesic in Diff(R) beginning at the identity, then φt(Ω) (or φt(Mi)) provides a path ...
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We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of unique maximal completions. The condition is verified in several situations of interest. This leads to existence and uniqueness of maximal spacelike conformal bou...
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When a Hamiltonian system has a \Kinetic + Potential" structure, the resulting ow is locally a geodesic ow. But there may be singularities of the geodesic structure, so the local structure does not always imply that the ow is globally a geodesic ow. In order for a ow to be a geodesic ow, the underlying manifold must have the structure of a unit tangent bundle. We develop homological conditions ...
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This article is about the interplay between topological dynamics and differential geometry. One could ask how many informations of the geometry are carried in the dynamic of the geodesic flow. M. Paternain proved in [6] that an expansive geodesic flow on a surface implies that there are no conjugate points. Instead of regarding notions that describe chaotic behavior (for example expansiveness) ...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1996
ISSN: 0022-040X
DOI: 10.4310/jdg/1214457900