165 citations · 1.1k across the 59 of their papers we have counts for
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An account on links between Finsler and Lorentz Geometries for Riemannian Geometers
Miguel Ángel Javaloyes, Enrique Pendás-Recondo, Miguel Sánchez
Some links between Lorentz and Finsler geometries have been developed in the last years, with applications even to the Riemannian case. Our purpose is to give a brief description o…
A general model for wildfire propagation with wind and slope
Miguel Ángel Javaloyes, Enrique Pendás-Recondo, Miguel Sánchez
A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies and slope of the gr…
The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
Miguel Ángel Javaloyes, Miguel Sánchez, Fidel F. Villaseñor
A systematic development of the so-called Palatini formalism is carried out for pseudo-Finsler metrics of any signature. Substituting in the classical Einstein-Hilbert-Palatini…
Anisotropic connections and parallel transport in Finsler spacetimes
Miguel Ángel Javaloyes, Miguel Sánchez, Fidel F. Villaseñor
The general notion of anisotropic connections is revisited, including its precise relations with the standard setting of pseudo-Finsler metrics, i.e., the canonic nonlinea…
Applications of cone structures to the anisotropic rheonomic Huygens' principle
Miguel Á. Javaloyes, Enrique Pendás-Recondo, Miguel Sánchez
A general framework for the description of classic wave propagation is introduced. This relies on a cone structure determined by an intrinsic space of velocities of propaga…
On the definition and examples of cones and Finsler spacetimes
Miguel Angel Javaloyes, Miguel Sánchez
A systematic study of (smooth, strong) cone structures $\C$ and Lorentz-Finsler metrics is carried out. As a link between both notions, cone triples , where (resp…
Some criteria for Wind Riemannian completeness and existence of Cauchy hypersurfaces
Miguel Ángel Javaloyes, Miguel Sánchez
Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers…
Wind Riemannian spaceforms and Randers metrics of constant flag curvature
Miguel Angel Javaloyes, Miguel Sánchez
Recently, wind Riemannian structures (WRS) have been introduced as a generalization of Randers and Kropina metrics. They are constructed from the natural data for Zermelo navigatio…
Compact affine manifolds with precompact holonomy are geodesically complete
Luis Aké Hau, Miguel Sánchez
This note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact.
A note on the causal homotopy classes of a globally hyperbolic spacetime
Pablo Morales Álvarez, Miguel Sánchez
Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.
Wind Finslerian structures: from Zermelo's navigation to the causality of spacetimes
Erasmo Caponio, Miguel Angel Javaloyes, Miguel Sánchez
The notion of wind Finslerian structure is developed; this is a generalization of Finsler metrics where the indicatrices at the tangent spaces may not contain the zero vector. In t…
Finsler metrics and relativistic spacetimes
Miguel A. Javaloyes, Miguel Sánchez
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric…
Remarks on the completeness of trajectories of accelerated particles in Riemannian manifolds and plane waves
Anna Maria Candela, Alfonso Romero, Miguel Sánchez
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzi…
On the completeness of trajectories for some mechanical systems
Miguel Sánchez
The classical tools which ensure the completeness of vector fields and second order differential equations for mechanical systems are revisited. Possible extensions in three direct…
Completeness of trajectories of relativistic particles under stationary magnetic fields
Anna Maria Candela, Alfonso Romero, Miguel Sánchez
The second order differential equation on a Lorentzian manifold describes, in particular, the dynamics of particles und…
Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness
Erasmo Caponio, Anna Valeria Germinario, Miguel Sánchez
By using Stationary-to-Randers correspondence (SRC), a characterization of light and time-convexity of the boundary of a region of a standard stationary (n+1)-spacetime is obtained…
On the definition and examples of Finsler metrics
Miguel Angel Javaloyes, Miguel Sánchez
For a standard Finsler metric F on a manifold M, its domain is the whole tangent bundle TM and its fundamental tensor g is positive-definite. However, in many cases (for example, t…
Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds
J. L. Flores, J. Herrera, M. Sanchez
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary for a standard conformally stati…
Convex domains of Finsler and Riemannian manifolds
Rossella Bartolo, Erasmo Caponio, Anna Valeria Germinario +1
A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to b…
On the interplay between Lorentzian Causality and Finsler metrics of Randers type
Erasmo Caponio, Miguel Angel Javaloyes, Miguel Sanchez
We obtain some results in both Lorentz and Finsler geometries, by using a correspondence between the conformal structure (Causality) of standard stationary spacetimes on $M=\R\time…
Lorentzian manifolds isometrically embeddable in L^N
Olaf Müller, Miguel Sánchez
We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isome…
Causal boundaries and holography on wave type spacetimes
Miguel Sánchez
The notion of a causal boundary for a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT corresponde…
Geodesics in semi-Riemannian Manifolds: Geometric Properties and Variational Tools
Anna Maria Candela, Miguel Sánchez
Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, const…
An Invitation to Lorentzian Geometry
Olaf Müller, Miguel Sánchez
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of '…