Symplectic structures on groups of automorphisms of symmetric spaces (Q1077022)

The author investigates the geometry of symplectic structures on groups of automorphisms of symmetric spaces of affine connectedness. The main result (Theorem 1) says: If \({\mathfrak M}\) is a torsion-free space of affine connectedness, then there exists an n-parameter family \((n=\dim {\mathfrak M})\) of closed 2-forms \(\omega\) with \(d\omega =0\), on the principal fibering of frames over \({\mathfrak M}\).