时空中的五维切向量：II。微分几何法
Five-Dimensional Tangent Vectors in Space-Time: II. Differential-Geometric Approach
摘要：
在这一部分的系列五维切向量介绍了第一次作为等价类的参数化曲线，然后作为微分代数算子，作用于标量函数。然后，我检查他们的基本代数性质和他们的平行运输的特殊情况下，时空具有特殊的局部对称性。在此之后，我给出了与维曲线参数相关联的五维切向量的定义，并表明它们可以与第一部分（math-ph/9805004）中正式介绍的五维向量相识别。最后，我谈谈与五向量相关的微分形式。
英文摘要：
In this part of the series five-dimensional tangent vectors are introduced first as equivalence classes of parametrized curves and then as differential-algebraic operators that act on scalar functions. I then examine their basic algebraic properties and their parallel transport in the particular case where space-time possesses a special local symmetry. After that I give definition to five-dimensional tangent vectors associated with dimensional curve parameters and show that they can be identified with the five-vectors introduced formally in part I (math-ph/9805004). In conclusion I speak about differential forms associated with five-vectors.
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