论文标题
具有水平分布和统计歧管的仿射和共形浸
Affine and Conformal Submersions with Horizontal Distribution and Statistical Manifolds
论文作者
论文摘要
我们表明，对于仿射浸入$π：\ mathbf {m} \ longrightArrow \ mathbf {b} $带有水平分布的$，$ \ mathbf {b} $是统计流形，其统计流形，其统计流形$ \ m m i \ m m mathbf {m} $具有指标和连接。引入了与水平分布的综合浸入的概念，这是对水平分布的仿射沉浸的概括。然后证明了$（\ Mathbf {M}，\ nabla，g_m）$的必要条件，成为具有水平分布的保形沉团的统计歧管。对于曲线$π\circσ$获得的必要条件，是$ \ mathbf {b} $的地理位置，如果$σ$是$ \ mathbf {m Mathbf {m} $ for $π的地理位置与水平分布的共形浸入。此外，我们为切线束$ t \ mathbf {m} $获得了必要且充分的条件，以成为有关Sasaki Lift指标和完整的升力连接的统计歧管。
We show that, for an affine submersion $π: \mathbf{M}\longrightarrow \mathbf{B}$ with horizontal distribution, $\mathbf{B}$ is a statistical manifold with the metric and connection induced from the statistical manifold $\mathbf{M}$. The concept of conformal submersion with horizontal distribution is introduced, which is a generalization of affine submersion with horizontal distribution. Then proved a necessary and sufficient condition for $(\mathbf{M}, \nabla, g_M)$ to become a statistical manifold for a conformal submersion with horizontal distribution. A necessary and sufficient condition is obtained for the curve $π\circ σ$ to be a geodesic of $\mathbf{B}$, if $σ$ is a geodesic of $\mathbf{M}$ for $π: (\mathbf{M},\nabla) \longrightarrow (\mathbf{B},\nabla^*) $ a conformal submersion with horizontal distribution. Also, we obtained a necessary and sufficient condition for the tangent bundle $T\mathbf{M}$ to become a statistical manifold with respect to the Sasaki lift metric and the complete lift connection.
