After a brief review of the basic notions the paper defines the G^L-structuresand their partial ordering. On this basis, the paper proves the necessary and sufficientconditions for G^L-structures to form bounded latti...After a brief review of the basic notions the paper defines the G^L-structuresand their partial ordering. On this basis, the paper proves the necessary and sufficientconditions for G^L-structures to form bounded lattices.展开更多
A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR-...A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).展开更多
We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we...We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.展开更多
The concepts of logically constrained overall systems and subsystems of recon-structability analysis are introduced. Then the paper gave an important basis for furtherresearches of the author-the sufficient conditions...The concepts of logically constrained overall systems and subsystems of recon-structability analysis are introduced. Then the paper gave an important basis for furtherresearches of the author-the sufficient conditions for their structural representation graphsto become Boolean lattices, and proved it.展开更多
文摘After a brief review of the basic notions the paper defines the G^L-structuresand their partial ordering. On this basis, the paper proves the necessary and sufficientconditions for G^L-structures to form bounded lattices.
文摘A CR-structure on a 2n +1-manifold gives a conformal class of Lorentz metrics on the Fefferman S1-bundle. This analogy is carried out to the quarternionic conformal 3-CR structure (a generalization of quaternionic CR- structure) on a 4n + 3 -manifold M. This structure produces a conformal class [g] of a pseudo-Riemannian metric g of type (4n + 3,3) on M × S3. Let (PSp(n +1,1), S4n+3) be the geometric model obtained from the projective boundary of the complete simply connected quaternionic hyperbolic manifold. We shall prove that M is locally modeled on (PSp(n +1,1), S4n+3) if and only if (M × S3 ,[g]) is conformally flat (i.e. the Weyl conformal curvature tensor vanishes).
基金supported by the GRF7032/08P of the HKRGC, Hong KongNational Natural Science Foundation of China (Grant No. 10971156)
文摘We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ≥2 into any complex space Z. After lifting to the normalization of the subvariety F (Ω) Z, we prove that F must be the canonical projection map to the quotient space of Ω by a finite group of automorphisms. The approach is along the line of the works of Mok and Tsai by considering radial limits of bounded holomorphic functions derived from F and proving that proper holomorphic maps between bounded symmetric domains preserve certain totally geodesic subdomains. In contrast to the previous works, in general we have to deal with multivalent holomorphic maps for which Fatou’s theorem cannot be applied directly. We bypass the difficulty by devising a limiting process for taking radial limits of correspondences arising from proper holomorphic maps and by elementary estimates allowing us to define distinct univalent branches of the underlying multivalent map on certain subsets. As a consequence of our rigidity result, with the exception of Type-IV domains, any proper holomorphic map f : Ω→ D of Ω onto a bounded convex domain D is necessarily a biholomorphism. In the exceptional case where Ω is a Type-IV domain, either f is a biholomorphism or it is a double cover branched over a totally geodesic submanifold which can be explicitly described.
文摘The concepts of logically constrained overall systems and subsystems of recon-structability analysis are introduced. Then the paper gave an important basis for furtherresearches of the author-the sufficient conditions for their structural representation graphsto become Boolean lattices, and proved it.
