Related papers: On completeness and dynamics of compact Brinkmann …
Let $X$ be a zero-dimensional locally compact Hausdorff space not necessarily metric and $G$ a compactly generated topological group not necessarily abelian or countable. We define recurrence at a point for any continuous action of $G$ on…
Kundt spacetimes are of great importance to General Relativity. We show that a Kundt spacetime is a Lorentz manifold with a non-singular isotropic geodesic vector field having its orthogonal distribution integrable and determining a totally…
In this article, we study geometric and analytical features of complete noncompact $\rho$-Einstein solitons, which are self-similar solutions of the Ricci-Bourguignon flow. We study the spectrum of the drifted Laplacian operator for…
We prove that the Kuznetsov--Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups $\mathrm{Sp}(2n,\mathbb{C})$ are full and consist of vector bundles. To achieve this, we construct several classes of…
We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building…
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion…
In this paper we give a new proof, valid for all dimensions, of the classical Herglotz-Noether theorem that all rotational shear-free and expansion-free flows (rotational Born-rigid flows) in Minkowski spacetime are generated by Killing…
We prove that in any spacetime dimension and under the null energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant…
Answering a problem posed by the second author on Mathoverflow, we prove that the connected countable Hausdorff spaces constructed by Bing and Ritter are topologically homogeneous.
We report a new symmetry of the Einstein-Friedmann equations for spatially flat Friedmann- Lema\^itre-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for…
We construct examples of compact homogeneous Riemannian manifolds admitting an invariant Bismut connection that is Ricci flat and non-flat, proving in this way that the generalized Alekseevsky-Kimelfeld theorem does not hold. The…
In this paper we have investigated some aspects of gradient $\rho$-Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient $\rho$-Einstein soliton is isometric to the Euclidean sphere by…
A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for…
We contribute to an original problem studied by Hamilton and others, in order to understand the behaviour of maximal solutions of the Ricci flow both in compact and non-compact complete orientable Riemannian manifolds of finite volume. The…
The problem of description of superintegrable systems (i.e., systems with closed trajectories in a certain domain) in the class of rotationally symmetric natural mechanical systems goes back to Bertrand and Darboux. We describe all…
Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with…
We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally…
The main result is the construction of ergodic transversal measures of full support on the space of all k-surfaces of a compact hyperbolic 3-manifold. This space is a laminated space, each of its leaf being identified with a "complete"…
In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the…
The procedure underlying the matching of 1-form (tetrad) fields in theories possessing absolute parallelism -- f(T) gravity being within this category -- is addressed and exemplified. We show that the remnant symmetries of the intervening…