Displaying similar documents to “The metrics of a twodimensional space with geodesics represented by a linear equation”

Infinite geodesic rays in the space of Kähler potentials

Claudio Arezzo, Gang Tian (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults...

Reachable sets for a class of contact sub-lorentzian metrics on ℝ³, and null non-smooth geodesics

Marek Grochowski (2008)

Banach Center Publications

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We compute future timelike and nonspacelike reachable sets from the origin for a class of contact sub-Lorentzian metrics on ℝ³. Then we construct non-smooth (and therefore non-Hamiltonian) null geodesics for these metrics. As a consequence we deduce that the sub-Lorentzian distance from the origin is continuous at points belonging to the boundary of the reachable set.

Hierarchy of integrable geodesic flows.

Peter Topalov (2000)

Publicacions Matemàtiques

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A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.

Geodesic graphs in Randers g.o. spaces

Zdeněk Dušek (2020)

Commentationes Mathematicae Universitatis Carolinae

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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.

Lorentzian geometry in the large

John Beem (1997)

Banach Center Publications

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Lorentzian geometry in the large has certain similarities and certain fundamental differences from Riemannian geometry in the large. The Morse index theory for timelike geodesics is quite similar to the corresponding theory for Riemannian manifolds. However, results on completeness for Lorentzian manifolds are quite different from the corresponding results for positive definite manifolds. A generalization of global hyperbolicity known as pseudoconvexity is described. It has important...