Related papers: Three-dimensional conformally symmetric manifolds

We consider complete Riemannian $3$-manifolds whose Ricci tensors have constant eigenvalues $(\lambda, \lambda, 0)$. When $\pi_1$ is finitely generated, we classify the topology of such manifolds by showing that they have a free fundamental…

We show that holomorphic riemannian metrics on compact complex threefolds are locally homogeneous (the pseudogroup of local isometries acts transitively on the manifold).

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…

On a compact foliated Riemannian manifold with some transversal curvature conditions, there are no nontrivial basic harmonic forms (M. Min-Oo et al., J. Reine Angew. Math. 415 (1991). In this paper, we extend the above facts to a complete…

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian metrics with all possible connected…

In this paper, we bend a closed Riemannian manifold in the conformal class, through solving a fully nonlinear equation. As a result, we prove that each metric of quasi-negative Ricci curvature is conformal to a metric with negative Ricci…

We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension $n$ of the conformally nonflat conformal…

The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…

We prove that some symetric semi-riemannian manifolds do not admit a proper domain which is divisible by the action of a discrete group of isometries. In other words, if a closed semi-riemannian manifold is locally isometric to such a…

In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have developed a Lorentzian version of the Quantum Regge Calculus in which the significant differences between simplices in Lorentzian signature and Euclidean signature are…

In this paper, we study the symmetries and perform other geometric analyses of the wave equation on some spacetimes {with non diagonal metric $g_{ij}$ which are of neutral signatures}. Wave equations on the standard Lorentzian manifolds…

We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of…

It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the…

In this paper, we give the Cartan's formula for half-lightlike submanifolds of Lorentzian manifolds and use it to show that a screen homothetic half-lightlike submanifolds of a Lorentzian space form, with a conformal co-screen distribution…

In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a…

The paper is devoted to metric connections with parallel skew-symmetric torsion in Lorentzian signature. This is motivated by recent progress in the Riemannian signature and by possible applications to supergravity theories. We provide a…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…

We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered…

This proceeding presents a synthesis of recent results on the emergence of pseudo-Riemannian structures from twisted spectral triples within the almostcommutative framework. It provides a unified algebraic mechanism for addressing the…

The present paper is devoted to questions located at the junction of the theory of space quasiconformal mappings and Riemannian surfaces. Theorems on local behavior of one class of open discrete mappings with unbounded characteristic of…