四川大学学报（自然科学版）
四川大學學報（自然科學版）
사천대학학보（자연과학판）
JOURNAL OF SICHUAN UNIVERSITY（NATURAL SCIENCE EDITION）
2008年
1期
1-9
,共9页
仿射K(a)hler流形%欧氏完备
倣射K(a)hler流形%歐氏完備
방사K(a)hler류형%구씨완비
affine K(o)hler manifold%euclidean completeness
设(M,g)为紧致仿射K(a)hler流形,仿射K(a) hler度量g=∑fijdxidxj.作者证明了若f满足Δlog(det(fij ))=0及 Ricci曲率半正定,则M是Rn/Γ,其中Γ为Rn上离散等距子群.进一步,对光滑函数h,作者考虑M上的变分问题,其E uler-Lagrange方程为Δlog(det(fij))=4h(det(fij))-(1)/(2 ),通过解这个四阶方程的一类边值问题,构造了定义在R n上的欧氏完备仿射K(a)hler流形.
設(M,g)為緊緻倣射K(a)hler流形,倣射K(a) hler度量g=∑fijdxidxj.作者證明瞭若f滿足Δlog(det(fij ))=0及 Ricci麯率半正定,則M是Rn/Γ,其中Γ為Rn上離散等距子群.進一步,對光滑函數h,作者攷慮M上的變分問題,其E uler-Lagrange方程為Δlog(det(fij))=4h(det(fij))-(1)/(2 ),通過解這箇四階方程的一類邊值問題,構造瞭定義在R n上的歐氏完備倣射K(a)hler流形.
설(M,g)위긴치방사K(a)hler류형,방사K(a) hler도량g=∑fijdxidxj.작자증명료약f만족Δlog(det(fij ))=0급 Ricci곡솔반정정,칙M시Rn/Γ,기중Γ위Rn상리산등거자군.진일보,대광활함수h,작자고필M상적변분문제,기E uler-Lagrange방정위Δlog(det(fij))=4h(det(fij))-(1)/(2 ),통과해저개사계방정적일류변치문제,구조료정의재R n상적구씨완비방사K(a)hler류형.
Let (M, g) be a n dimenional compact affine K(o)hler manifold, its K(o)hler metric is g=∑fijdxidxj.If Δlog(det(fij))=0 and its Ricci curvature Rij0, then M must be Rn/Γ, where Γ be a subgroup of isometric of Rn which acts freely and properly discontinuously on Rn. Moreover, for a smooth function h, a more general volume variational problem on M is considered, the Euler-Lagrange equation is Δlog(det(fij))=4h(det(fij))-(1)/(2), by solving some boundary problem of the 4-order equation, many Euclidean complete affine K(o)hler manifold are constructed.
