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Curves in Lorentzian spaces

E. Nešović, M. Petrović-Torgašev, L. Verstraelen (2005)

Bollettino dell'Unione Matematica Italiana

The notion of ``hyperbolic'' angle between any two time-like directions in the Lorentzian plane L 2 was properly defined and studied by Birman and Nomizu [1,2]. In this article, we define the notion of hyperbolic angle between any two non-null directions in L 2 and we define a measure on the set of these hyperbolic angles. As an application, we extend Scofield's work on the Euclidean curves of constant precession [9] to the Lorentzian setting, thus expliciting space-like curves in L 3 whose natural equations...

Dégénerescence locale des transformations conformes pseudo-riemanniennes

Charles Frances (2012)

Annales de l’institut Fourier

Nous étudions l’ensemble Conf ( M , N ) des immersions conformes entre deux variétés pseudo-riemanniennes ( M , g ) et ( N , h ) . Nous caractérisons notamment l’adhérence de Conf ( M , N ) dans l’espace des applications continues 𝒞 0 ( M , N ) , et décrivons quelques propriétés géométriques de ( M , g ) lorsque cette adhérence est non triviale.

Diffeomorphisms constructively associated with mutually diverging spacetimes which allow a natural identification of event points in general relativity. Part II

Gaetano Zampieri (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro si dà una definizione di divergenza fra cronotopi della Relatività Generale e si costruisce un criterio per l'identificazione dei punti eventi di cronotopi divergenti che appartengono ad una classe consistente con la presenza di campi elettromagnetici nel vuoto.

Distinguished connections on ( J 2 = ± 1 ) -metric manifolds

Fernando Etayo, Rafael Santamaría (2016)

Archivum Mathematicum

We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of ( J 2 = ± 1 ) -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...

Einstein-Weyl structures on lightlike hypersurfaces

Cyriaque Atindogbe, Lionel Bérard-Bergery, Carlos Ogouyandjou (2013)

Open Mathematics

We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.

Feuilletages totalement géodésiques, flots riemanniens et variétés de Seifert

Pierre Mounoud (2005)

Annales de l’institut Fourier

Nous étudions les feuilletages lisses totalement géodésiques de codimension 1 des variétés lorentziennes. Nous nous intéressons notamment aux relations entre les flots riemanniens et les feuilletages géodésiques. Nous prouvons que, quitte à prendre un revêtement d’ordre 2 , tout fibré de Seifert possède un tel feuilletage.

Foliations of lightlike hypersurfaces and their physical interpretation

Krishan Duggal (2012)

Open Mathematics

This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined...

Formes normales pour les champs conformes pseudo-riemanniens

Charles Frances, Karin Melnick (2013)

Bulletin de la Société Mathématique de France

Nous établissons des formes normales pour les champs conformes sur une variété pseudo-riemannienne, au voisinage d’une singularité. Sur une variété lorentzienne analytique, nous montrons qu’ou bien un tel champ est linéarisable au voisinage de la singularité, ou bien la variété est conformément plate. Dans tous les cas, le champs est localement conjugué à une forme normale sur un espace modèle. Pour des métriques lisses de signature quelconque, nous obtenons un résultat analogue sous l’hypothèse...

Currently displaying 61 – 80 of 317