Resumen de Invariant metric f-structures on specific homogeneous reductive spaces

Anna Sakovich

• For homogeneous reductive spaces G=H with reductive complements decompos- able into an orthogonal sum m = m1©m2©m3 of three Ad(H)-invariant irreducible mutually inequivalent submodules we establish simple conditions under which an invariant metric f- structure (f; g) belongs to the classes G1f , NKf, and Kill f of generalized Hermitian geom- etry. The statements obtained are then illustrated with four examples. Namely we consider invariant metric f-structures on the manifolds of oriented °ags SO(n)=SO(2) £ SO(n ¡ 3) (n ¸ 4), the Stiefel manifold SO(4)=SO(2), the complex °ag manifold SU(3)=Tmax, and the quaternionic °ag manifold Sp(3)=SU(2) £ SU(2) £ SU(2).