1,720,983 research outputs found
Geodesics on Lorentzian manifold with convex boundary Nonlinear Anal. 47 (2001), 3543-3548.
No full textGeodesics in stationary spacetimes and classical Lagrangian systems
No full textWe state a fundamental correspondence between geodesics on stationary spacetimes and the equations
of classical particles on Riemannian manifolds, accelerated by a potential and a magnetic field. By varia-
tional methods, we prove some existence and multiplicity theorems for fixed energy solutions (joining two
points or periodic) of the above described Riemannian equation. As a consequence, we obtain existence and
multiplicity results for geodesics with fixed energy, connecting a point to a line or periodic trajectories, in
(standard) stationary spacetimes
Orthogonal trajectories on Riemannian manifolds and applications to Plane Wave type spacetimes
No full textWe present a result on trajectories of a Lagrangian system joining two given submanifolds of a
Riemannian manifold, under the action of an unbounded potential. As an application, we consider geodesics
in a class of semi-Riemannian manifolds, the Plane Wave type spacetimes
Existence and multiplicity results for massive particles trajectories in a universe with boundary
No full textTrajectories of a charge in a magnetic field on Riemannian manifolds with boundary
No full textWe prove an existence result for trajectories of classical particles accelerated
by a potential and a magnetic field on a non–complete Riemannian manifold M . Both the
potential and the magnetic field may be not bounded and have critical growth. We state
a suitable convexity assumption involving the magnetic field in order to prove that the
support of each trajectory is entirely contained in M
Convexity conditions on the boundary of a stationary spacetime and applications
No full textWe deal with the convexity of the boundary of a standard stationary spacetime L =
M × R. We obtain a characterization of this notion by means of Riemannian conditions
involving a potential plus a magnetic field on M , where both are linked to the coefficients
of the metric. Natural applications of our results concern geodesics having a prescribed
parametrization proportional to the arc length, joining a point to a line and periodic,
on non-complete manifolds, and in particular on Kerr spacetime
Timelike spatially closed trajectories under a potential on splitting Lorentzian manifolds
No full textWe study the periodic motions of a relativistic particle submitted
to the action of an external potential V . On a wide class of Lorentzian manifolds,
we find timelike solutions of a differential equation (depending on V ) closed in the
spatial component and satisfying a Dirichlet condition in the temporal one. We
prove a multiplicity result for the critical points of the (strongly indefinite) functional
associated to the problem, using a saddle type theorem based on the notion of relative
category. The periodicity of the problem, the non–compactness of the manifold and
the lack of some assumptions involving the relative category make necessary to use a
suitable penalization scheme and a Galerkin approximation
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