Open problems and questions about geodesics

K Burns, VS Matveev - Ergodic Theory and Dynamical Systems, 2021 - cambridge.org
The paper surveys open problems and questions related to geodesics defined by
Riemannian, Finsler, semi-Riemannian and magnetic structures on manifolds. It is an …

A curvature inequality characterizing totally geodesic null hypersurfaces

B Olea - Mediterranean Journal of Mathematics, 2023 - Springer
A well-known application of the Raychaudhuri equation shows that, under geodesic
completeness, totally geodesic null hypersurfaces are unique which satisfy that the Ricci …

[HTML][HTML] Canonical variation of a Lorentzian metric

B Olea - Journal of Mathematical Analysis and Applications, 2014 - Elsevier
Given a Lorentzian manifold (M, g L) and a timelike unitary vector field E, we can construct
the Riemannian metric g R= g L+ 2 ω⊗ ω, ω being the metrically equivalent one form to E …

A note on geodesic vector fields

S Deshmukh, J Mikeš, NB Turki, GE Vîlcu - Mathematics, 2020 - mdpi.com
The concircularity property of vector fields implies the geodesicity property, while the
converse of this statement is not true. The main objective of this note is to find conditions …

Equigeodesics on flag manifolds

N Cohen, L Grama, CJC Negreiros - arXiv preprint arXiv:0904.3770, 2009 - arxiv.org
This paper provides a characterization of homogeneous curves on a geometric flag manifold
which are geodesic with respect to any invariant metric. We call such curves homogeneous …

Closed geodesics in Lorentzian surfaces

S Suhr - Transactions of the American Mathematical Society, 2013 - ams.org
We show that every closed Lorentzian surface contains at least two closed geodesics.
Explicit examples show the optimality of this claim. Refining this result we relate the least …

On closed geodesics in Lorentz manifolds

S Allout, A Belkacem, A Zeghib - Geometric and Functional Analysis, 2024 - Springer
On Closed Geodesics in Lorentz Manifolds | Geometric and Functional Analysis Skip to
main content SpringerLink Account Menu Find a journal Publish with us Track your …

Actions of discrete groups on stationary Lorentz manifolds

P Piccione, A Zeghib - Ergodic Theory and Dynamical Systems, 2014 - cambridge.org
We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike
Killing vector field, and whose isometry group has infinitely many connected components …

A Counterexample to Guillemin's Zollfrei Conjecture

S Suhr - Journal of Topology and Analysis, 2013 - World Scientific
A COUNTEREXAMPLE TO GUILLEMIN'S ZOLLFREI CONJECTURE Page 1 Journal of Topology
and Analysis Vol. 5, No. 3 (2013) 251–260 c© World Scientific Publishing Company DOI …

On the isometry group and the geometric structure of compact stationary Lorentzian manifolds

P Piccione, A Zeghib - arXiv preprint arXiv:1002.0814, 2010 - arxiv.org
We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike
Killing vector field, and whose isometry group has infinitely many connected components …