Bismut Ricci 平坦双扭曲积埃尔米特流形

Bismut Ricci Flat Doubly WarpedProduct Hermitian Manifold

摘要: 设(M₁,g)和(M₂,h)是两个埃尔米特流形, 双扭曲积埃尔米特流形 (_f2M₁ × _f1M₂,G) 是赋予了扭曲积埃尔米特度量G= f₂²g + f₁²h的乘积流形M₁ × M₂，其中f₁和f₂分别是M₁和M₂上的正值光滑函数。 本文给出双扭曲积埃尔米特流形的Bismut联络、Bismut曲率、Bismut Ricci曲率和Bismut标量曲率的表达式，并得到双扭曲积埃尔米特流形 Bismut Ricci 平坦的充要条件，从而给出构造 Bismut Ricci 平坦埃尔米特流形的有效方法。

Abstract: Let (M₁，g) and (M₂，h) be two Hermitian manifolds, the doubly warped product Hermitian manifold  (_f2M₁ × _f1M₂，G) is the product manifold M₁ × M₂ endowed with the warped product Hermitian metric G= f₂²g + f₁²h, where f1 and f2 are positive smooth functions on M₁ and M₂, respectively. In this paper, we obtain the formulae of Bismut connection, Bismut curvature, Bismut Ricci curvature and Bismut scalar curvature of doubly warped product Hermitian manifold. The necessary and suffcient condition for doubly warped product Hermitian manifold to be Bismut Ricci at is given. Thus, we provide an effctive way to construct Bismut Ricci at Hermitian manifold.