Singularity classes of special 2-flags.
Six-dimensional considerations of Einstein's connection for the first two-classes. I: The recurrence relations in 6--UFT.
Size minimizing surfaces
We prove a new existence theorem pertaining to the Plateau problem in -dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.
Ski de fond
Smooth singular solutions of hyperplane fields. I
Smooth singular solutions of hyperplane fields. II
Smooth structures on fibre jet spaces
Smoothness and geometry of boundaries associated to skeletal structures I: sufficient conditions for smoothness
We introduce a skeletal structure in , which is an - dimensional Whitney stratified set on which is defined a multivalued “radial vector field” . This is an extension of notion of the Blum medial axis of a region in with generic smooth boundary. For such a skeletal structure there is defined an “associated boundary” . We introduce geometric invariants of the radial vector field on and a “radial flow” from to . Together these allow us to provide sufficient numerical conditions for...
Soldered double linear morphisms
Our aim is to show a method of finding all natural transformations of a functor into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps commuting with -soldered automorphisms of a double vector space are investigated. On the set of such mappings, appropriate partial operations are introduced. The natural transformations are bijectively related with the elements...
Some algebraic theorems on vector-valued forms and their geometric applications
Some aspects of the homogeneous formalism in field theory and gauge invariance
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...
Some estimates of integrals with a composition operator.
Some functorial prolongations of general connections
We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket.
Some further results on lifts of linear vector fields related to product preserving gauge bundle functors on vector bundles
We present some lifts (associated to a product preserving gauge bundle functor on vector bundles) of sections of the dual bundle of a vector bundle, some derivations and linear connections on vector bundles.
Some geometric aspects of the calculus of variations in several independent variables
This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.
Some higher order operations with connections
Some higher order operations with connections (Preliminary communication)
Some liftings of Poisson structures to Weil bundles
We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
Some Natural Constructions on Vector Fields and Higher Order Cotangent Bundles.
Some natural operators on vector fields
We determine all natural operators transforming vector fields on a manifold to vector fields on , , and all natural operators transforming vector fields on to functions on , . We describe some relations between these two kinds of natural operators.