The dynamics of external force free motion of pendulums on surfaces of constant Gaussian curvature is addressed when the pivot moves along a geodesic obtaining the Lagrangian of the system. As an application it is possible ...

The study of maximal hypersurfaces in Lorentzian manifolds is an interesting mathematical problem, which connects di_erential geometry, nonlinear partial di_erential equations and certain problems in mathematical relativity. ...

Through a new technique, we provide uniqueness, rigidity and non-existence results for compact minimal submanifolds of arbitrary dimension in a large class of Riemannian manifolds, which include between others, Riemannian ...

We analyze the concept of uniformly accelerated observer in Galilean spacetimes in the context of Newton–Cartan theory and find natural geometric assumptions to ensure that an inextensible uniformly accelerated observer ...

In this paper we introduce a new general approach for the study of spacetimes admitting a standard static splitting. This approach allows us to give an alternative proof for the uniqueness of splitting in the spatially ...

We introduce two different ways to establish the concept of infinitesimal position vector field between “infinitesimally nearby” observers in a Galilean spacetime as well as show their mathematical equivalence. We also use ...

In this work we introduce a new family of non-relativistic spacetimes: standard stationary Galilean spacetimes, which constitute the local geometric model of stationary Galilean spacetimes. We also study the geodesic ...

We obtain new simple sufficient conditions to ensure the stability and strong stability of maximal hypersurfaces (without boundary) immersed in an arbitrary spacetime. Several applications to maximal hypersurfaces in a ...