affine connection

On the Duality Connection of the Flat Affine Connection

平坦仿射联络的对偶联络

Curvature tensor of an affine connection

仿射联络的曲率张量

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 .

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。

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 .

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。