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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...

Complex geodesics and isometries in Cartan domains of type four

Edoardo Vesentini (1995)

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

Holomorphic maps of Cartan domains of type four preserving the supports of complex geodesics are characterized, providing, in particular, a new description of holomorphic isometries.

Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents

Fanghua Lin, Tristan Rivière (1999)

Journal of the European Mathematical Society

There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S 1 -valued function defined on the boundary of a bounded regular domain of R n . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...

Complex methods in real integral geometry

Eastwood, Michael (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations M Ω η Ω ˜ @ > τ > > X ( Ω complex manifold; M totally real, real-analytic submanifold;...

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