Opuscula Mathematica
Opuscula Math. 25, no. 2 (2005), 287-298

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

Yarema A. Prykarpatsky
Anatoliy M. Samoilenko
Anatoliy K. Prykarpatsky
Abstract. 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 quations are presented.
Keywords: Hamiltonian reduction, symplectic structures, connections, principal fiber bundles, Yang-Mills type gauge fields.
Mathematics Subject Classification: 34A30, 34B05, 34B15.
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Yarema A. Prykarpatsky
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
Anatoliy M. Samoilenko
The Institute of Mathematics, NAS, Kyiv 01601, Ukraine
Anatoliy K. Prykarpatsky
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
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Received: 2004-11-14.
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Yarema A. Prykarpatsky, Anatoliy M. Samoilenko, Anatoliy K. Prykarpatsky, The geometric properties of reduced canonically symplectic spaces with symmetry, their relationship with structures on associated principal fiber bundles and some applications. Part 1, Opuscula Math. 25, no. 2 (2005), 287-298, http://dx.doi.org/10.7494/OpMath.2005.25.2.287.
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