仿射联络

平坦仿射联络的对偶联络

On the Duality Connection of the Flat Affine Connection

仿射联络的曲率张量

Curvature tensor of an affine connection

统计流形在一定的不变原则下被证明具有唯一的黎曼度量，即为Fisher信息阵，以及一对对偶的仿射联络。

Under the invariance principle , the manifold is proved to have a unique Riemannian metric given by the Fisher information matrix , and a dual pairs of affine connections .

讨论了FisherZ分布流形的对偶结构及其平坦性，进而给出了该流形的黎曼度量、α仿射联络和α曲率，并在该统计流形上定义了散度来衡量两点之间的距离；

A dual affine structure is constructed on it and a divergence is defined as a distance like measure . Furthermore , the Riemannian metric , α - connections and α - curvatures of the Fisher Z manifold are given .

某一类齐性仿射联络空间

A certain class of homogeneous spaces of affine connections

具有面积测度的一些仿射联络空间

Certain affinely connected spaces with areal metric

共轭的仿射联络的扩充

An extension of conjugate affine connections

关于某类非线性系统共振情形的研究某一类齐性仿射联络空间

Resonant oscillation of a certain nonlinear system a certain class of homogeneous spaces of affine connections

本文给出仿射联络空间中仿射运动群的基本定理的一种证明；

This paper gives a proof about the fundamental theorem ( and the inverse theorem ) on the affine groups of motions in the affinely connected spaces .

本文给出了平坦仿射联络的对偶联络的定义，并推导出形状算子S~、仿射基本形h~以及横截联络形式r~的表示式。

The definition of the duality connection of the flat affine connection is given and the representations of the shape operator S , the affine fundamental form h and the transversal connection form τ are obtained .

利用力学控制系统的仿射联络模型的内在几何齐次结构和李代数结构，研究了系统的短时间局部能控性，其中，系统的拉格朗日函数取为系统的动能。

Relying on the inherent geometric homogeneous and Lie algebraic structure for the affine connection model of mechanical control systems with kinetic energy Lagrangian , the small - time local controllability for the systems is explored .