两类特殊的双扭曲积埃尔米特流形

Two Special Types of Doubly Warped Product Hermitian Manifold

设(M_(1),g)和(M_(2),h)是两个埃尔米特流形,双扭曲积埃尔米特流形(f_(2)M_(1)×f_(1)M_(2),G)是赋予了扭曲积埃尔米特度量G=f_(2)^(2)g+f_(1)^(2)h的乘积流形M_(1)×M_(2),其中f_(1)和f_(2)分别是M_(1)和M_(2)上的正值光滑函数。文章给出双扭曲积埃尔米特流形的挠率表达式,得到双扭曲积埃尔米特流形是凯勒流形或平衡流形的充要条件,并在特定条件下给出双扭曲积埃尔米特流形满足弱爱因斯坦条件的充要条件。

Let(M_(1),g)and(M_(2),h)be two Hermitian manifolds,the doubly warped product(abbreviated as DWP)Hermitian manifold(f_(2) M_(1)×f_(1)M_(2),G)endowed with the warped product Hermitian metric G=f_(2)^(2)g+f_(1)^(2)h,where f_(1)and f_(2) are positive smooth functions on M_(1)and M_(2),respectively.In this paper,the torsion expression of DWP-Hermitian manifold is given.Necessary and sufficient conditions for DWP-Hermitian manifold are Kähler or balanced manifold.Under certain conditions,we obtain a necessary and sufficient condition for a DWP-Hermitian manifold satisfying weak Einstein condition.