Periodic trajectories on Lorentz manifolds under the action of a vector field

DOI10.1006/JDEQ.2000.3776zbMath0971.58010OpenAlexW1964323327MaRDI QIDQ1586121

Rossella Bartolo, Maria Tucci, Elvira Mirenghi

Publication date: 28 October 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3776

zbMATH Keywords

geodesicsperiodic trajectorystatic Lorentz manifold

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of global differential geometry to the sciences (53C80) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (3)

Stationary Lorentz manifolds and vector fields: existence of periodic trajectories ⋮ Time-like solutions to the Lorentz force equation in time-dependent electromagnetic and gravitational fields ⋮ Lusternik-Schnirelman theory for the action integral of the Lorentz force equation

Cites Work

• On the existence of multiple geodesics in static space-times
• The imbedding problem for Riemannian manifolds
• Trajectories connecting two events of a Lorentzian manifold in the presence of a vector field
• On the existence of infinitely many geodesics on space-time manifolds
• On the existence of infinitely many trajectories for a class of static Lorentzian manifolds like Schwarzschild and Reissner-Nordström space-times
• Periodic solutions with prescribed energy on non-complete Riemannian manifolds
• Category of loop spaces of open subsets in euclidean space
• General relativity and cosmology
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