Stable complex structures on real manifolds

Poisson Structures on Complex Flag Manifolds Associated with Real Forms

For a complex semisimple Lie group G and a real form G0 we define a Poisson structure on the variety of Borel subgroups of G with the property that all G0-orbits in X as well as all Bruhat cells (for a suitable choice of a Borel subgroup of G) are Poisson submanifolds. In particular, we show that every non-empty intersection of a G0-orbit and a Bruhat cell is a regular Poisson manifold, and we ...

Stable Complex Manifolds

1. T. Van de Ven [3] has recently shown that there exist real 4dimensional manifolds which admit almost complex structures but admit no complex structures, e.g. SXS* # SXS # CP(2). The purpose of this note is to show that this is an unstable phenomenon. Let M be a C w-dimensional real manifold without boundary and let TM be its tangent bundle. R is real Euclidean fe-space and C is complex &-spa...

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

Manifolds with Many Complex Structures

Stable Exponentially Harmonic Maps Between Finsler Manifolds