Differential geometrical relations for a class of formal series

• Autorzy: Alexandr Baranovitch
• Języki publikacji: EN

Abstrakty

EN

An extension of the category of local manifolds is considered. Instead of smooth mappings of neighbourhoods of linear spaces as morphisms we deal with formal operator power series (or formal maps). Analogues of the objects appearing on smooth manifolds and vector bundles (vector fields, sections of a bundle, exterior forms, the de Rham complex, connection, etc.) are considered in this way. All the examinations are carried out in algebraic language, for we do not care about the convergence of formal maps. It may be useful for the investigation of some nonlinear differential equations.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 279-287

Daty

wydano

1997

Twórcy

autor

Alexandr Baranovitch

• National Technical University of Ukraine, 37 Peremogy prosp., Kiev, Ukraine

Bibliografia

• [1] M. N. Araslanov, Yu. L. Daletskiǐ, Composition Logarithm in the Class of Formal Operator Power Series, Funct. Anal. Appl. 26 (1992), 57-60.
• [2] A. M. Baranovitch, Yu. L. Daletskiǐ, Differential-Geometric Relations for Formal Operator Power Series Class, Preprint.
• [3] Yu. L. Daletskiǐ, Algebra of Compositions and Non-Linear Equations, appear.
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• [6] M. Gerstenhaber, The Cohomology Structure of an Associative Ring, Ann. Math 78 (1963), 59-103.
• [7] C. Godbillon, Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969.