数学进展
數學進展
수학진전
ADVANCES IN MATHEMATICS
2007年
6期
686-692
,共7页
凸性%度量的等价%超Cartan域
凸性%度量的等價%超Cartan域
철성%도량적등개%초Cartan역
convexity%equivalence of metrics%super-Cartan domain
首先证明超Cartan域YI(k;N;m,n)为凸域的充分必要条件是2k(≧)m;接着讨论了在超Cartan域上四类经典的不变度量,即Bergman度量、Caratheodory度量、Kobayashi度量和Einstein-Kahler度量的等价性;最后通过计算得到了超Cartan域YI(1;N;2,n)和YI(2;N;2,n)上的Caratheodory度量(和Kobayashi度量)的显表达式.
首先證明超Cartan域YI(k;N;m,n)為凸域的充分必要條件是2k(≧)m;接著討論瞭在超Cartan域上四類經典的不變度量,即Bergman度量、Caratheodory度量、Kobayashi度量和Einstein-Kahler度量的等價性;最後通過計算得到瞭超Cartan域YI(1;N;2,n)和YI(2;N;2,n)上的Caratheodory度量(和Kobayashi度量)的顯錶達式.
수선증명초Cartan역YI(k;N;m,n)위철역적충분필요조건시2k(≧)m;접착토론료재초Cartan역상사류경전적불변도량,즉Bergman도량、Caratheodory도량、Kobayashi도량화Einstein-Kahler도량적등개성;최후통과계산득도료초Cartan역YI(1;N;2,n)화YI(2;N;2,n)상적Caratheodory도량(화Kobayashi도량)적현표체식.
We first prove the convexity on YI(k;N;m,n),the super-Cartan domain of the first type when 2k(≥)m,and then we study the equivalence of the Bergman metric,Caratheodory metric, Kobayashi metric and Einstein-Kahler metric and the holomorphic curvatures of Caratheodory metric(and Kobayashi metric).We also calculate the Caratheodory metric(and Kobayashi metric) of YI(1;N;2,n)and YI(2;N;2,n).