Families of \((1,2)\)-symplectic metrics on full flag manifolds (Q1607898)

The result of \textit{A. Lichnerowicz} [Sympos. Math., Roma 3, 341--402 (1970; Zbl 0193.50101)] states that a holomorphic map from a Riemann surface to a \((1,2)\)-symplectic manifold is harmonic. Let \(F(n)\) be the full flag manifold \( U(n)/ U(1) \times \dots \times U(1)\). Lichnerowicz's result motivates the search of \((1,2)\)-symplectic metrics on \(F(n)\). Extending results by Borel, Eells and Salamon, Mo and Negreiros, the author constructs new \((1,2)\)-symplectic invariant metrics on \(F(n)\).