Holomorphic bi-disks in 9-dimensional CR hypersurfaces with Levi signature (2,2) must satisfy two complex torsion equations, and a concrete hypersurface is shown to violate one of them.
Equivalences of 5-dimensional CR-manifolds IV: Six ambiguity matrix groups (Initial G-structures)
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abstract
Class I CR manifolds have initial G-structure a certain 4-dimensional subgroup of GL_3(C). Class II CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_4(C). Class III-1 CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_5(C). Class III-2 CR manifolds have initial G-structure a certain 18-dimensional subgroup of GL_5(C). Class IV-1 CR manifolds have initial G-structure a certain 13-dimensional subgroup of GL_5(C). Class IV-2 CR manifolds have initial G-structure a certain 10-dimensional subgroup of GL_5(C).
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Holomorphic immersions of bi-disks into $9$ dimensional real hypersurfaces with Levi signature $(2, 2)$
Holomorphic bi-disks in 9-dimensional CR hypersurfaces with Levi signature (2,2) must satisfy two complex torsion equations, and a concrete hypersurface is shown to violate one of them.