The Riemannian curvature tensor and differentiable spaces
The structure of smooth mappings over Weil algebras and the category of manifolds over algebras.
The structure of tangentors and their morphisms
The super complex Frobenius theorem
We formulate and prove a super analogue of the complex Frobenius theorem of Nirenberg.
The Supetrace on the Grassmann envelope M(m,n;Λ)
The tangent bundle of -velocities over a homogeneous space
The tangent space and the arcwise tangent space to a differential space
The tangent stars of a set, and extensions of smooth functions.
The topology of integrable differential forms near a singularity
The torsion of spinor connections and related structures.
The total divergence equation.
The vertical prolongation of the projectable connections
We prove that any first order F2 Mm1,m2,n1,n2-natural operator transforming projectable general connections on an (m1,m2, n1, n2)-dimensional fibred-fibred manifold p = (p, p) : (pY : Y → Y) → (pM : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on V Y → M.
Théorème de Kirchhoff et théorie de Hodge
Théorème d'existence et d'unicité pour un système d'equations aux dérivées partielles non-linéaire.
Théorie des opérateurs différentiels gradués sur les formes différentielles
There exists a prolongation functor of infinite order
Theta Functions Defined by Geodesic Cycles in Quotients of SU(P,1).
Three natural generalizations of Fedosov quantization.
To the question about the maximum principle for manifolds over local algebras.
Top-Dimensional Group of the Basic Intersection Cohomology for Singular Riemannian Foliations
It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an example of a singular isometric flow for which the top-dimensional basic cohomology group is non-trivial, but the basic cohomology does not satisfy...