具有芬斯勒特征的AP结构：I
An Ap-Structure with Finslerian Flavor: I
摘要：
构造了一种既具有绝对平行性又具有Finsler性质的几何结构（FAP结构）。该结构的构建块被假定为位置和方向的函数。非线性连接自然出现，并根据结构的构建块进行定义。利用FAP的非线性联络定义了两个线性联络，一个是Berwald型，另一个是Cartan型。两个线性连接都是非对称的，因此允许扭转。度量张量是根据结构的构建块来定义的。得到了该度量为Finslerian度量的条件。并给出了FAP-空间为AP-1的条件。
英文摘要：
A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges naturally and is defined in terms of the building blocks of the structure. Two linear connections, one of Berwald type and the other of the Cartan type, are defined using the non-linear connection of the FAP. Both linear connections are non-symmetric and consequently admit torsion. A metric tensor is defined in terms of the building blocks of the structure. The condition for this metric to be a Finslerian one is obtained. Also, the condition for an FAP-space to be an AP-one is given.
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