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

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