一类拟凸域的不变Kahler度量与.pdfVIP

406 Y Vol.40, No. 6 199711 ACTA MATHEMATICA SINICA Nov., 1997
ktYRO K¨ahler owr    (TBKJZw 100037)  Cm+n  K¨ahler  ! #$%()* fV  K¨ahler  !#$% MR(1991) +j 32A07 ,j O174.56 Invariant K¨ahler Metrics and Curvatures on a Class of Pseudoconvex Domains Yin Weiping Tong Wu (Department of Mathematics, Capital Normal University, Beijing 100037, China) Abstract For a class of pseudoconvex domains E , the Aut(E)-invariant K¨ahler metrics, its curvatures and Aut(E)-invariant harmonic functions are given in the explicit forms. Keywords Pseudoconvex domain, Invariant K¨ahler metric, Curvature, Invariant har- monic function 1991 MR Subject Classification 32A07 Chinese Library Classification O174.56 tAxd E = E (m, n, K ) = {(z, w) ∈ Cn+m : |z |2 + |w |2K 1}, n n m 2 2 2K z = (z , · · · , z ) ∈ C , w = (w , · · · , w ) ∈ C , K 0, |z | = zz = |z | , |w | = 1 n 1 m j j =1 m K K 2 (ww ) = |wj | . j =1 K = 1 L E (m, n, 1) k Cn+m n K 1 L E (m, n, K ) kCd Levi O m R m = 1 LRCdKL E (1, n, K), nJvzZ [1−4] . E m 1 E (m, n, K ) R “decoupled” (W decoupled q [5]). FWoEA Derridj-Tartakoff[6] EE ∂-Neumann saug (Analytic hypoellipticity), Kodama[7] S EcU D’Angelo[8] Bergman WzOo [9] Bergman C Kobayashi CtrRo [1, 2] E E (1, n, K) zZfX E (m, n, K ) y WIG K¨ahler