Locally transitive tournaments and the classification of {$(1,2)$}-symplectic metrics on maximal flag manifolds

Families of (1,2)-symplectic Metrics on Full Flag Manifolds

Real Groups Transitive on Complex Flag Manifolds

Let Z = G/Q be a complex flag manifold. The compact real form Gu of G is transitive on Z. If G0 is a noncompact real form, such transitivity is rare but occasionally happens. Here we work out a complete list of Lie subgroups of G transitive on Z and pick out the cases that are noncompact

O ct 2 00 0 Families of ( 1 , 2 ) – Symplectic Metrics on Full Flag Manifolds ∗

We obtain new families of (1,2)–symplectic invariant metrics on the full complex flag manifolds F (n). For n ≥ 5, we characterize n−3 different n–dimensional families of (1,2)–symplectic invariant metrics on F (n). Any of these families corresponds to a different class of non–integrable invariant almost complex structure on F (n).

Classification of Flag-Transitive Steiner Quadruple Systems

A Steiner quadruple system of order v is a 3 − (v, 4, 1) design, and will be denoted SQS(v). Using the classification of finite 2-transitive permutation groups all SQS(v) with a flag-transitive automorphism group are completely classified, thus solving the ”still open and longstanding problem of classifying all flag-transitive 3− (v, k,1) designs” (cf. [5, p. 273], [6]) for the smallest value o...

Quasi-potentials and Kähler–Einstein metrics on flag manifolds, II

For a homogeneous space G/P , where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler–Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kähler–Einstein metric, thus enabling us to com...