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Almost invariant submanifolds for compact group actions

Alan Weinstein (2000)

Journal of the European Mathematical Society

We define a C 1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G , there is a G -invariant submanifold C 1 -close to N . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...

Classification of principal connections naturally induced on W 2 P E

Jan Vondra (2008)

Archivum Mathematicum

We consider a vector bundle E M and the principal bundle P E of frames of E . Let K be a principal connection on P E and let Λ be a linear connection on M . We classify all principal connections on W 2 P E = P 2 M × M J 2 P E naturally given by K and Λ .

Enveloppe galoisienne d'une application rationnelle de P1.

Guy Casale (2006)

Publicacions Matemàtiques

In 2001, B. Malgrange defines the D-envelope or galoisian envelope of an analytical dynamical system. Roughly speaking, this is the algebraic hull of the dynamical system. In this short article, the D-envelope of a rational map R: P1 --> P1 is computed. The rational maps characterised by a finitness property of their D-envelope appear to be the integrable ones.

Espace de twisteurs d’une variété presque hermitienne de dimension 6

Jean-Baptiste Butruille (2007)

Annales de l’institut Fourier

On s’intéresse à l’espace de twisteurs réduit d’une variété presque hermitienne, en relisant un article de N.R.O’Brian et J.H.Rawnsley (Ann. Global Anal. Geom., 1985). On traite la question laissée ouverte de la dimension 6. Cet espace est muni d’une structure presque complexe 𝒥 en utilisant la distribution horizontale de la connexion hermitienne canonique. On montre qu’une condition nécessaire d’intégrabilité de 𝒥 est que la variété soit de type  W 1 W 4 dans la classification de Gray et Hervella. Dans...

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