Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8
We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. ...
Real Algebraic Geometry and the 17th Hilbert Problem.
Real commutative algebra. III. Dedekind-Weber-Riemann manifolds.
The space S of all non-trivial real places on a real function field K|k of trascendence degree one, endowed with a natural topology analogous to that of Dedekind and Weber's Riemann surface, is shown to be a one-dimensional k-analytic manifold, which is homeomorphic with every bounded non-singular real affine model of K|k. The ground field k is an arbitrary ordered, real-closed Cantor field (definition below). The function field K|k is thereby represented as a field of real mappings of S which might...
Recent advances in the theory of holonomy
Reducibility theorems for differentiable liftings in fiber bundles
Réduction de Birkhoff des 1-formes différentielles à partie singulière bien adaptée et à coefficients à valeurs dans une algèbre de Lie libre
On étudie, dans cet article, la simplification analytique d’une forme de Pfaff fermée à valeurs dans une algèbre de Lie libre, au voisinage d’une singularité. On montre que cette réduction est possible pour une grande classe de formes : les formes à partie singulière bien adaptée. Cette classe contient (strictement) la plupart des situations étudiées jusqu’ici. On montre aussi, que les séries non commutatives utilisées convergent si leurs éléments sont voisins de zéro dans une algèbre normée complète....
Reduction in contact geometry.
Reduction theorem for general connections
We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.
Regular analytic arcs and curves
Regular and coregular mappings of differential spaces
Régularité et non régularité des solutions non strictement convexes de l'équation de Monge-Ampère
Regularity conditions for liftings of functions and vector fields to natural bundles
Regularity of differential forms minimizing degenerate elliptic functionals.
Relations between constants of motion and conserved functions
We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.
Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold.
Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold
All natural operations transforming linear connections on the tangent bundle of a fibred manifold to connections on the 1-jet bundle are classified. It is proved that such operators form a 2-parameter family (with real coefficients).
Relèvement linéaire des cobords
Remark on bilinear operations on tensor fields
This short note completes the results of [3] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [3] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.
Remark on local existence of -structure with prescribed structural functions on a manifold of dimension two