Galilean geometry of motions.
Gauge natural constructions on higher order principal prolongations
Let be a principal prolongation of a principal bundle P → M. We classify all gauge natural operators transforming principal connections on P → M and rth order linear connections on M into general connections on . We also describe all geometric constructions of classical linear connections on from principal connections on P → M and rth order linear connections on M.
Gauge natural prolongation of connections
The main result is the classification of all gauge bundle functors H on the category which admit gauge natural operators transforming principal connections on P → M into general connections on HP → M. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to HP → P. A special attention is paid to linear connections.
Genera of Ramified Coverings.
General construction of Banach-Grassmann algebras
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
Generalización de la forma de Liouville - Aplicaciones.
Generalization of p-regularity notion and tangent cone description in the singular case
The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
Generalized differential forms over an operand and algebraic models of fibrations. (Formes différentielles généralisées sur une opérade et modéles algébriques des fibrations.)
Generic one-step bracket-generating distributions of rank four
We give a uniform, explicit description of the generic types of one–step bracket–generating distributions of rank four. A manifold carrying such a structure has dimension at least five and no higher than ten. For each of the generic types, we give a brief description of the resulting class of generic distributions and of geometries equivalent to them. For dimensions different from eight and nine, these are available in the literature. The remaining two cases are dealt with in my doctoral thesis.
Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
Geometric approach to Goursat flags
Geometric classes of Goursat flags and the arithmetics of their encoding by small growth vectors
Goursat distributions are subbundles, of codimension at least 2, in the tangent bundles to manifolds having the flag of consecutive Lie squares of ranks not depending on a point and growing-very slowly-always by 1. The length of a flag thus equals the corank of the underlying distribution. After the works of, among others, Bryant&Hsu (1993), Jean (1996), and Montgomery&Zhitomirskii (2001), the local behaviours of Goursat flags of any fixed length r≥2 are stratified into geometric classes...
Geometric construction of the Levi-Civita parallelism.
Geometric objects of submanifolds of a space with fundamental Lie pseudogroup
Geometric objects with finitely determined germs
Geometric versions of Whitney regularity for smooth stratifications
Geometrical aspects of the covariant dynamics of higher order
We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra, [7]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations.
Geometrical properties of prolongation functors
Géométrie sous-riemannienne
Geometrische Bedingungen für die Integrabilität von Vektor-Feldern auf Teilmengen.