The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal, fiber bundles and some applications. Pt. 1

• Autorzy: Prykarpatsky Y.A. , Samoilenko A.M. , Prykarpatsky A.K.
• Języki publikacji: EN

Abstrakty

EN

The canonical reduction method on canonically symplectic manifolds is analized in detail, the relationships with the geometric properties of associated principal fiber bundles endowed with connection structures are stated. Some results devoted to studying geometrical properties of nonabelian Yang-Mills type gauge field equations are presented.

Słowa kluczowe

EN

Hamiltonian reduction; symplectic structures; connections; principal fiber bundles; Yang-Mills type gauge fields

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 2
• Strony: 287--298
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Prykarpatsky Y.A.

• The Institute of Mathematics, NAS, Kyiv 01601, Ukraine; AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
• The Institute of Mathematics, NAS, Kyiv 01601, Ukraine

autor

Samoilenko A.M.

• The Institute of Mathematics, NAS, Kyiv 01601, Ukraine

autor

Prykarpatsky A.K.

• AGH University of Science and Technology, Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

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• [4] Kummer J.: On the construction of the Reduced phase space of a Hamiltonian system with symmetry. Indiana University Mathem. Journal, 30(1981), N2, 281-281.
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• [8] Kupershmidt B. A.: Infinite-dimensional analogs of the minimal coupling prin­ciple and of the Poincare lemma for differential two-forms. Diff. Geom. & Appl. (1992) 2, 275-293.
• [9] Marsden J., Weinstein A.: The Hamiltonian structure of the Maxwell-Vlasov equations. Physica D (1982) 4, 394-406.
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