摘要
设(M,g)为紧致仿射Khler流形,仿射Kahler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Euler-Lagrange方程为Δlog(det(fij))=4h(det(fij))-12,通过解这个四阶方程的一类边值问题,构造了定义在Rn上的欧氏完备仿射Kahler流形.
Let (M, g) be a n dimenional compact affine Kaehler manifold, its Kaehler metric is g=∑fijdxidxj If Δlog(det(fij)) = 0 and its Ricci curvature Rij≥0, then M must be R^n/Г, where Г be a subgroup of isometric of R^n which acts freely and properly discontinuously on R^n. Moreover, for a smooth function h, a more general volume variational problem on M is considered, the Euler-Lagrange equation is Alog(det(fij ))= 4h (det(f/ij))^-1/2, by solving some boundary problem of the 4-order equation, many Euclidean complete affine Kaehler manifold are constructed.
出处
《四川大学学报(自然科学版)》
CAS
CSCD
北大核心
2008年第1期1-9,共9页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(10401026)