摘要
首先,我们考虑二个例外Cartan 域的酉几何.得到了它们的Bergman 核函数、Cauchy-Szeg(?)核、Poisson 核和Bergman 度量的显表达式.其次,我们对维数为n 的Cartan 域R,给出了一类不变微分算子:若R 的Bergman 度量为ds^2=(?)则(?)的所有j 阶主子式之和}在尺的双全纯映照下是不变的.我们也得到了Li(u)的解的显表达等等.
Firstly,we consider the unitary geometry of two exceptional Car-tan domains R_V(16)and R_(VI)(27).We obtain the explicit formulas ofBergman kernel function,Cauchy-Szeg(?) kernel,Poinsson kernel andBergman metric for R_V(16)and R_(VI)(27).Secondly,we give a class of invariant differential operators forCartan domain R of dimension n:If the Bergman metric of R is(?)thenL_i(u)={The sum of all principal minors of degree j for L(u)} isinvariant under the biholomorphic mapping of R.We also obtain theexplicit solutions of L_i(u)(j=1,2,…,n)and so on.
基金
Partially supported by grant from Science Research Foundation ofAcademia Sinica.
