E. E. Levi convexity and the Hans Lewy problem. Part I : reduction to vanishing theorems
Equivalence problem for minimal rational curves with isotrivial varieties of minimal rational tangents
We formulate the equivalence problem, in the sense of É. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form an isotrivial family. The main question in this case is for which projective variety , a family of minimal rational curves with -isotrivial varieties of minimal rational tangents...
Espaces variationnels et mécanique
Ce travail est essentiellement consacré aux systèmes dynamiques non conservatifs, la force généralisée dépendant à la fois des paramètres de position et de vitesse . désignant l’espace-temps de configuration, l’espace fibré des vecteurs tangents, celui des directions tangentes à , on caractérise par son lagrangien homogène et le tenseur-force antisymétrique dont le produit contracté par le vecteur vitesse donne le vecteur force généralisé.Dans la première partie, on étudie l’algèbre...
Explicit expression of Cartan’s connection for Levi-nondegenerate 3-manifolds in complex surfaces, and identification of the Heisenberg sphere
We study effectively the Cartan geometry of Levi-nondegenerate C 6-smooth hypersurfaces M 3 in ℂ2. Notably, we present the so-called curvature function of a related Tanaka-type normal connection explicitly in terms of a graphing function for M, which is the initial, single available datum. Vanishing of this curvature function then characterizes explicitly the local biholomorphic equivalence of such M 3 ⊂ ℂ2 to the Heisenberg sphere ℍ3, such M’s being necessarily real analytic.
Exterior differential systems for Yang-Mills theories.