四川大学学报（自然科学版）2008，Vol.45Issue(1)：1-9,9.
仿射K(a)hler流形的一类变分问题
Some variational problems for affine K(a)hler manifold
摘要
Abstract
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.关键词
仿射K(a)hler流形/欧氏完备Key words
affine K(o)hler manifold, euclidean completeness分类
数理科学引用本文复制引用
杨宝莹,王宝富..仿射K(a)hler流形的一类变分问题[J].四川大学学报（自然科学版）,2008,45(1):1-9,9.基金项目
国家自然科学基金(10401026) （10401026）
