| 仿射K(a)hler流形的一类变分问题 |
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| 引用本文： | 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) |
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| 作者姓名： | 杨宝莹 王宝富 |
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| 摘 要： | 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.
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| 关 键 词： | 仿射K(a)hler流形 欧氏完备 affine K(o)hler manifold euclidean completeness 仿射 流形 变分问题 affine variational problems Euclidean complete boundary problem equation general volume smooth function isometric Ricci curvature manifold compact 欧氏完备 构造 边值问题 四阶方程 作者考 |
Some variational problems for affine K(a)hler manifold |
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| YANG Bao-Ying,WANG Bao-Fu. Some variational problems for affine K(a)hler manifold[J]. Journal of Sichuan University (Natural Science Edition), 2008, 45(1) |
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| Authors: | YANG Bao-Ying WANG Bao-Fu |
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| 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. |
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| Keywords: | affine K(o)hler manifold euclidean completeness |
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