论文标题
自我仿制的黑森和保友kähler歧管
Selfsimilar Hessian and conformally Kähler manifolds
论文作者
论文摘要
令$（m，\ nabla，g）$为Hessian歧管。然后，切线捆绑$ tm $的总空间可以赋予kähler结构$ \ left（i，{\ cal g} \ right）$。我们说，同质的Hessian歧管是Hessian歧管$（m，\ nabla，g）$，并具有$ g $保留$ \ nabla $和$ g $的$ g $ g $的传递动作。如果$（m，\ nabla，g）$是组$ g $的简单连接的均质的Hessian歧管，那么我们构建了$ g \ltimes_θ\ Mathbb {r}^n $ on $ tm = m \ times \ times \ times \ times \ times \ times \ times \ mathbb {r}^r}^n $ ag y hous y hous hous y hous hous hous y house（组$ g \ltimes_θ\ mathbb {r}^n $。自我仿制的黑森歧管是带有同一个矢量场$ξ$的Hessian歧管。令$（m，\ nabla，g，ξ）$为简单连接的自我仿制的hessian歧管，以便$ξ$已完成，$ g $是$（m，\ nabla，g，ξ）$的一组自动形态，使得$ g $在级别的级别上行为$ {g（g（eC））。然后，我们在$ tm $上构建同质的kähler结构。
Let $(M,\nabla,g)$ be a Hessian manifold. Then the total space of the tangent bundle $TM$ can be endowed with a Kähler structure $\left(I,{\cal g}\right)$. We say that a homogeneous Hessian manifold is a Hessian manifold $(M,\nabla,g)$ endowed with a transitive action of a group $G$ preserving $\nabla$ and $g$. If $(M,\nabla,g)$ is a simply connected homogeneous Hessian manifold for a group $G$ then we construct an action of the group $G\ltimes_θ\mathbb{R}^n$ on $TM=M\times \mathbb{R}^n$ such that $\left(TM,I,g\right)$ is a homogeneous Kähler manifold for the group $G\ltimes_θ\mathbb{R}^n$. A selfsimilar Hessian manifold is a Hessian manifold endowed with a homothetic vector field $ξ$. Let $(M,\nabla,g,ξ)$ be a simply connected selfsimilar Hessian manifold such that $ξ$ is complete and $G$ be a group of automorphisms of $(M,\nabla,g,ξ)$ such that $G$ acts transitively on the level line ${g(ξ,ξ)=1}$. Then we construct homogeneous conformally Kähler structure on $TM$.
