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We investigate the $CR$ geometry of the orbits $M$ of a real form $G_0$ of a complex simple group $G$ in a complex flag manifold $X=G/Q$. We are mainly concerned with finite type, Levi non-degeneracy conditions, canonical $G_0$-equivariant and Mostow fibrations, and topological properties of the orbits.
We study, from the point of view of CR geometry, the orbits M of a real form G of a complex semisimple Lie group G in a complex flag manifold G/Q. In particular we characterize those that are of finite type and satisfy some Levi nondegeneracy conditi
Given a complex manifold $X$, any Kahler class defines an affine bundle over $X$, and any Kahler form in the given class defines a totally real embedding of $X$ into this affine bundle. We formulate conditions under which the affine bundles arising t
We compute the Euler-Poincare characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.
This note establishes smooth approximation from above for J-plurisubharmonic functions on an almost complex manifold (X,J). The following theorem is proved. Suppose X is J-pseudoconvex, i.e., X admits a smooth strictly J-plurisubharmonic exhaustion f
Let $(X,omega)$ be a compact Kahler manifold of dimension $n$ and fix $1leq mleq n$. We prove that the total mass of the complex Hessian measure of $omega$-$m$-subharmonic functions is non-decreasing with respect to the singularity type. We then solv