# Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics

@inproceedings{Gao2021LocalOM, title={Local orthogonal maps and rigidity of holomorphic mappings between real hyperquadrics}, author={Yung Gao and Sui-chung. Ng}, year={2021} }

We introduced a new coordinate-free approach to study the Cauchy-Riemann (CR) maps between the real hyperquadrics in the complex projective space. The central theme is based on a notion of orthogonality on the projective space induced by the Hermitian structure defining the hyperquadrics. There are various kinds of special linear subspaces associated to this orthogonality which are well respected by the relevant CR maps and this is where the rigidities come from. Our method allows us to…

## One Citation

On the rank of Hermitian polynomials and the SOS Conjecture

- Mathematics
- 2021

Let z ∈ C and ‖z‖ be its Euclidean norm. Ebenfelt proposed a conjecture regarding the possible ranks of the Hermitian polynomials in z, z̄ of the form A(z, z̄)‖z‖2, known as the SOS Conjecture, where…

## References

SHOWING 1-10 OF 18 REFERENCES

Super-rigidity for holomorphic mappings between hyperquadrics with positive signature

- Mathematics
- 2005

We study local holomorphic mappings sending a piece of a real hyperquadric in a complex space into a hyperquadric in another complex space of possibly larger dimension. We show that these mappings…

Rigidity of Proper Holomorphic Maps Among Generalized Balls with Levi-Degenerate Boundaries

- Mathematics
- 2021

In this paper we studied a broader type of generalized balls which are domains on the complex projective with possibly Levi-degenerate boundaries. We proved rigidity theorems for proper holomorphic…

Proper holomorphic mappings on flag domains of SU(p,q)-type on projective spaces

- Mathematics
- 2013

Rigidity for proper holomorphic mappings among SU(p, q)-type flag domains (also known as generalized balls) on projective spaces is obtained. We prove that the mappings are linear when the signature…

Cycle spaces of flag domains on Grassmannians and rigidity of holomorphic mappings

- Mathematics
- 2012

We study certain cycle spaces on flag domains of SU(p, q)-type on Grassmannians and their relations with the rigidity of holomorphic mappings between Grassmannians. Rigidity is obtained for those…

A hyperplane restriction theorem for holomorphic mappings and its application for the gap conjecture

- Mathematics
- 2021

We established a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by the corresponding theorem of Green for OPn(d). Our theorem allows us…

Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces

- Mathematics
- 1998

We prove that a germ of a holomorphic map f between C n and C n ' sending one real-algebraic submanifold MC n into another M ' � C n ' is algebraic provided Mcontains no complex-analytic discs and M…

Obstructions to embeddability into hyperquadrics and explicit examples

- Mathematics
- 2008

We give series of explicit examples of Levi-nondegenerate real-analytic hypersurfaces in complex spaces that are not transversally holomorphically embeddable into hyperquadrics of any dimension. For…

Holomorphic mappings between hyperquadrics with small signature difference

- Mathematics
- 2009

In this paper, we study holomorphic mappings sending a hyperquadric of signature $\ell$ in ${\Bbb C}^n$ into a hyperquadric of signature $\ell'$ in ${\Bbb C}^N$. We show (Theorem 1.1) that if the…

Mapping B n into B 2 n − 1

- Mathematics
- 2001

In this paper, we are concerned with the classification problem of proper holomorphic maps between balls in complex spaces. Write Bn = {z ∈ Cn : |z| < 1} and Prop(Bn, BN ) for the collection of all…