论文标题
从双重连接到几乎接触结构
From Dual Connections to Almost Contact Structures
论文作者
论文摘要
平滑的Riemaniann歧管$ M $上的二元结构是三重$（m，g，\ nabla）$，带有$ g $ a riemaniann吨和$ \ nabla $ a offine Connection，通常假定为扭转。从$ g $和$ \ nabla $，可以定义双连接$ \ nabla^*$，并且三重$（m，\ nabla，\ nabla^*）$称为统计歧管，这是信息几何学中的基本对象。在这项工作中，我们根据此概念给出条件，以便将几乎接触结构和某些相关结构接受：在三维情况下，几乎接触度量，接触，接触度量，触点，宇宙骨骼和Cokähler。
A dualistic structure on a smooth Riemaniann manifold $M$ is a triple $(M,g,\nabla)$ with $g$ a Riemaniann metric and $\nabla$ an affine connection, generally assumed to be torsionless. From $g$ and $\nabla$, the dual connection $\nabla^*$ can be defined and the triple $(M, \nabla,\nabla^*)$ is called a statistical manifold, a basic object in information geometry. In this work, we give conditions based on this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric,contact, contact metric, cosymplectic, and coKähler in the three-dimensional case.
