论文标题
具有卓越的自动组的扭曲的产品歧管
Warped-like product manifolds with exceptional holonomy groups
论文作者
论文摘要
在本文中，我们与特殊类型的度量结构相关的$ g_2 $和$ spin（7）$几何形状，我们称之为扭曲的产品指标。我们提出了一般的类似扭曲的产品指标的Ansatz，作为扭曲的产品的定义。考虑到纤维碱的分解，通过允许纤维度量为非对角线，扭曲的产物的定义被认为是多磁管歧管的概括。在某些特殊情况下，我们提供了$（3+3+2）的明确示例，$ spin（7）$ spin（7）$ holomany的形式的$ m = f \ times b $，其中基本$ b $是二维的riemannian歧管Riemannian $ 3 $ -Manifolds。此外，还研究了$（3+3+1）$（3+3+1）的明确示例，$ g_2 $ hulonomy。从文献来看，本研究还提供了其他一些具有$ G_2 $ holomony的特殊类似扭曲的产品指标。我们认为，我们的类似扭曲的产品指标的方法将是使用扭曲和多重磁性产品结构的几何形状的重要概念，尤其是具有卓越的全体性质的流形。
In this paper we review $G_2$ and $Spin(7)$ geometries in relation with a special type of metric structure which we call warped-like product metric. We present a general ansatz of warped-like product metric as a definition of warped-like product. Considering fiber-base decomposition, the definition of warped-like product is regarded as a generalization of multiply-warped product manifolds, by allowing the fiber metric to be non block diagonal. For some special cases, we present explicit example of $(3+3+2)$ warped-like product manifolds with $Spin(7)$ holonomy of the form $M=F\times B$, where the base $B$ is a two dimensional Riemannian manifold, and the fibre $F$ is of the form $F=F_1\times F_2$ where $F_i$'s $(i=1,2)$ are Riemannian $3$-manifolds. Additionally an explicit example of $(3+3+1)$ warped-like product manifold with $G_2$ holonomy is studied. From the literature, some other special warped-like product metrics with $G_2$ holonomy are also presented in the present study. We believe that our approach of the warped-like product metrics will be an important notion for the geometries which use warped and multiply-warped product structures, and especially manifolds with exceptional holonomy.
