Horizontal structures on fibre manifolds
How Charles Ehresmann's vision of geometry developed with time
In the mid fifties, Charles Ehresmann defined Geometry as "the theory of more or less rich structures, in which algebraic and topological structures are generally intertwined". In 1973 he defined it as the theory of differentiable categories, their actions and their prolongations. Here we explain how he progressively formed this conception, from homogeneous spaces to locally homogeneous spaces, to fibre bundles and foliations, to a general notion of local structures, and to a new foundation of differential...
How to define "convex functions" on differentiable manifolds
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: . if M is a linear manifold, then (M) contains convex functions, . (·) is invariant under diffeomorphisms, . each f ∈ (M) is differentiable on a dense -set, is investigated.
Hypersurfaces of Prescribed Mean Curvature over Obstacles.
Ideals of the Lie algebras of vector fields
Implicit quasilinear differential systems: A geometrical approach.
In the heart of representable metric jets
Induced differential forms on manifolds of functions
Differential forms on the Fréchet manifold of smooth functions on a compact -dimensional manifold can be obtained in a natural way from pairs of differential forms on and by the hat pairing. Special cases are the transgression map (hat pairing with a constant function) and the bar map (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
Infinitely many solutions for a boundary value problem with discontinuous nonlinearities.
Infinitesimal and local structures for Banach spaces and its exponentials in a topos
Infinitesimal automorphisms of distributions
Infinitesimal computations in topology
Infinitesimal differential geometry.
Infinitésimaux et intuitionnisme
Integral formulae associated with non-parameter invariant multiple integral problems of arbitrary order in the calculus of variations.
Intégrales asymptotiques et monodromie
Intégrales asymptotiques et monodromie
Intégrales itérées
Intégrales premières d'une forme de Pfaff analytique
Soit un germe en de 1-forme différentielle holomorphe vérifiant la condition d’intégrabilité . S’il existe un germe d’application holomorphe de dans qui possède les deux propriétés suivantes :a) a une intégrale première formelle,b) la codimension du lieu singulier de est supérieure ou égale à 2,alors a une intégrale première holomorphe.
Integration of differential forms on manifolds with locally finite variations.