Related papers: Generic metrics satisfy the generic condition
In this paper we develop new methods of study of generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres. We prove that for any…
We study the question of local and global uniqueness of completions, based on null geodesics, of Lorentzian manifolds. We show local uniqueness of such boundary extensions. We give a necessary and sufficient condition for existence of…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…
We consider a general scalar-tensor theory of gravity and review briefly different forms it can be presented (different conformal frames and scalar field parametrizations). We investigate the conditions under which its field equations and…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik \cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is close enough to the…
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…
We prove that generic solutions of the vacuum constraint Einstein equations do not possess any global or local space-time Killing vectors, on an asymptotically flat Cauchy surface, or on a compact Cauchy surface with mean curvature close to…
In these two lectures I describe the difficulties one encounters when trying to construct a framework in which to describe topology change in classical general relativity where one sticks to the assumption of an everywhere non-singular…
This letter describes a novel derivation of general relativity by considering the (non)self-consistency of theories whose Hamiltonians are constraints. The constraints, from Hamilton's equations, generate the evolution, while the evolution,…
Within a first-order framework, we comprehensively examine the role played by boundary conditions in the canonical formulation of a completely general two-dimensional gravity model. Our analysis particularly elucidates the perennial themes…
Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to…
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the $\gamma_k$ functions on the space of its hermitian metrics.
Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability…
We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.
On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. Moreover, this result may be localized to compact subdomains in…
The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory - general relativity. The inability to define complete initial data consistently and independently of future measurements,…
We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M=G/K is studied. We focus on the metrics at which the Ricci curvature map is, locally, as injective and surjective as it can be. Our main…