埃尔米特形式和自伴反线性算子对的标准形式
A canonical form for pairs consisting of a Hermitian form and a self-adjoint antilinear operator
摘要：
受超曲面型Cauchy-Riemann（CR）结构的局部微分几何中的一个问题的启发，我们找到了由非退化Hermitian型和自伴反线性算子组成的对，或等价地由非退化Hermitian型和对称双线性型组成的对的标准型.这推广了以前已知的关于这类对的同时正规化的结果，即Benedetti和Cragnolini（1984）关于在Hermite形式是正定的情况下这些对的同时对角化的结果，以及Hong和Horn（1986）的结果，其中给出了同时对角化的准则。
英文摘要：
Motivated by a problem in local differential geometry of Cauchy--Riemann (CR) structures of hypersurface type, we find a canonical form for pairs consisting of a nondegenerate Hermitian form and a self-adjoint antilinear operator, or, equivalently, consisting of a nondegenerate Hermitian form and a symmetric bilinear form. This generalizes the only previously known results on simultaneous normalization of such pairs, namely, the results of Benedetti and Cragnolini (1984) on simultaneous diagonalization of these pairs in the case where the Hermitian form is positive definite and of Hong and Horn (1986), where a criterion for simultaneous diagonalization is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
