超二次曲面间Segre映射的正交对和刚性问题
Orthogonal pair and a rigidity problem for Segre maps between hyperquadrics
摘要：
受\cite{GN1}中研究的正交映射的启发，引入了可能退化厄米型的射影空间之间的正交对.此外，正交对是实超二次曲面的Segre族之间的全纯Segre映射的推广。我们证明了在必要的余维限制下，非退化全纯正交对也具有一定的刚性性质。作为应用，我们得到了张在\cite{Zh}中得到的与Heisenberg超曲面有关的Segre映射的刚性定理.
英文摘要：
Being motivated by the orthogonal maps studied in \cite{GN1}, orthogonal pairs between the projective spaces equipped with possibly degenerate Hermitian forms were introduced. In addition, orthogonal pairs are generalizations of holomorphic Segre maps between Segre families of real hyperquadrics. We showed that non-degenerate holomorphic orthogonal pairs also have certain rigidity properties under a necessary codimension restriction. As an application, we got a rigidity theorem for Segre maps related to Heisenberg hypersurfaces obtained by Zhang in \cite{Zh}.
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