Related papers: Periodic Geodesics and Geometry of Compact Lorentz…
We analyze a class of 5D non-compact warped-product spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the so-called canonical coordinate gauge of Mashhoon et al. We…
We prove that the topology, smooth structure, and metric of a compact Lorentzian manifold with boundary is uniquely determined by data at the boundary. The data consists of the lengths and directions of future-directed once-broken geodesics…
Motivated by supersymmetry methods in general relativity, we study four-dimensional Lorentzian space-times with a complex Dirac spinor field satisfying a Killing-spinor-like equation where the Killing constant is promoted to a complex…
In this paper, we construct a geometrical compactification of the geodesic flow of non-compact complete hyperbolic surfaces $\Sigma$ without cusps having finitely generated fundamental group. We study the dynamical properties of the…
We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds…
We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the…
A rank $m$ symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the first integral of the geodesic flow which is a degree $m$…
We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse…
We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then…
We study the isometry groups of (non-compact) Lorentzian manifolds with well-behaved causal structure, aka causal spacetimes satisfying the ``no observer horizons'' condition. Our main result is that the group of time orientation-preserving…
Given a compact K\"ahler manifold (X,\omega_0), according to Mabuchi, the set of K\"ahler forms cohomologous to \omega_0 has the natural structure of an infinite dimensional Riemannian manifold. We address the question whether points in…
We show that conformal vector fields on compact locally conformally product manifolds are orthogonal to the flat distribution and Killing with respect to the Gauduchon metric.
In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous…
We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up…
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that…
We investigate harmonic unit vector fields with totally geodesic integral curves on 3-manifolds. Under mild curvature assumptions, we classify both the vector fields and the manifolds that support them. Our results are inspired by…
We revisit the notion of massive particle hypersurfaces and place it within a unified framework alongside photon hypersurfaces in stationary spacetimes. More precisely, for Killing-invariant timelike hypersurfaces $T=\mathbb{R}\times S_0$,…
In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of…
We formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. This result both transfers the corresponding statement for locally convex metric spaces established by S. Alexander and R. Bishop to the Lorentzian setting, and…