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Contact hamiltonians distinguishing locally certain Goursat systems

Piotr Mormul (2000)

Banach Center Publications

For the first time in dimension 9, the Goursat distributions are not locally smoothly classified by their small growth vector at a point. As shown in [M1], in dimension 9 of the underlying manifold 93 different local behaviours are possible and four irregular pairs of them have coinciding small growth vectors. In the present paper we distinguish geometrically objects in three of those pairs. Smooth functions in three variables - contact hamiltonians in the terminology of Arnold, [A] - help to do...

Continuous transformation groups on spaces

K. Spallek (1991)

Annales Polonici Mathematici

A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies...

Coomologia di un campo vettoriale mai nullo

Angela De Sanctis, Giuliano Sorani (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We write a cohomological resolution of the sheaf 𝒮 of solutions of the differential operator ∂ / ∂ ⁡ x n on a manifold M and study the cohomology groups H 0 ⁢ ( M , 𝒮 ) and H 1 ⁢ ( M , 𝒮 ) .

Curvature and the equivalence problem in sub-Riemannian geometry

Erlend Grong (2022)

Archivum Mathematicum

These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which...

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