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Geodesics in Asymmetic Metric Spaces

Andrea C. G. Mennucci (2014)

Analysis and Geometry in 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.

Yiming Long (1995)

Mathematische Zeitschrift

Geodesics on product lorentzian manifolds

F. Giannoni, A. Masiello (1995)

Annales de l'I.H.P. Analyse non linéaire

Geodesics Satisfying General Boundary Conditions

Karsten Grove (1973)

Commentarii mathematici Helvetici

Geometrical decomposition of the free loop space on a manifold with finitely many closed geodesics.

Morgenstern, Thomas (1997)

Georgian Mathematical Journal

Géométrie sous-riemannienne

Ivan Kupka (1995/1996)

Séminaire Bourbaki

Geometry of the rolling ellipsoid

Krzysztof Andrzej Krakowski, Fátima Silva Leite (2016)

Kybernetika

We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....