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Complete classification of parallel Lorentz surfaces in neutral pseudo hyperbolic 4-space

Bang-Yen Chen (2010)

Open Mathematics

A Lorentz surface of an indefinite space form is called a parallel surface if its second fundamental form is parallel with respect to the Van der Waerden-Bortolotti connection. Such surfaces are locally invariant under the reflection with respect to the normal space at each point. Parallel surfaces are important in geometry as well as in general relativity since extrinsic invariants of such surfaces do not change from point to point. Recently, parallel Lorentz surfaces in 4D neutral pseudo Euclidean...

Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

Bang-Yen Chen (2009)

Open Mathematics

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian...

Complétude et flots nul-géodésibles en géométrie lorentzienne

Pierre Mounoud (2004)

Bulletin de la Société Mathématique de France

On étudie la complétude géodésique des flots nul-prégéodésiques sur les variétés lorentziennes compactes, ce qui donne une obstruction à être nul-géodésique. On montre que lorsque l’orthogonal du champ de vecteurs engendrant le flot considéré s’intègre en un feuilletage , la complétude du flot se lit sur l’holonomie de . On montre ainsi qu’il n’existe pas de flots nul-géodésiques lisses sur S 3 . On montre aussi qu’un 2 -tore lorentzien est nul-complet si et seulement si ses feuilletages de type lumière...

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