On the CR-structure of compact group orbits associated with bounded symmetric domains

On the local equivalence of homogeneous CR-manifolds

“…The C * -equivalence classes of nonzero S-orbits in E are in 1-1-correspondence (compare [4] for details) with the elements of…”

“…Denote by M the set of all non-totally-real S-orbits in E where E runs through all types in the above list. In [4] the CR-structure of all M ∈ M has been intensively studied. In particular, for each such M the group Aut(M) (which is also the CR-homeomorphism group of M) has been explicitly determined and the global CR-equivalence problem for M has been solved: Suppose that M, M ∈ M are CR-isomorphic.…”

“…In [4] the Cauchy-Riemann structures of certain compact linear group orbits in C n have been studied, which arise in the context of bounded symmetric domains. Among others the (global) CR-equivalence problem for these orbits could be solved completely in [4], while the corresponding local problem was left open.…”

“…Among others the (global) CR-equivalence problem for these orbits could be solved completely in [4], while the corresponding local problem was left open.…”

“…To be more specific let us recall some facts from [4] for special cases: Fix integers 1 p < q and denote by E := C p×q the space of all complex p × q-matrices. Then the compact semi-simple Lie group G := SU(p) × SU(q) acts linearly on E by z → uzv −1 .…”