时空中的五维切向量：VI。双向量导数及其应用
Five-Dimensional Tangent Vectors in Space-Time: VI. Bivector Derivative and Its Application
摘要：
这是一系列论文的第六篇，也是最后一部分，其中前五篇已于1998年年中提交到目前的档案馆，并于1999年作为国家研究所的预印本出版。目前的论文也是作为INR预印本印刷的，但由于非科学原因，从未以任何形式公开，无论是电子版还是硬拷贝。在它中，我定义了任意黎曼几何情况下的四向量场和五向量场的双向量导数;研究了五向量仿射连接的更一般情况;引入了曲率张量的五向量模拟;并考虑了爱因斯坦和Kibble-Sciama方程可能的五向量推广。最后，我定义了非时空矢量和张量的双矢量导数，并推导出麦克斯韦方程的可能的五矢量推广。
英文摘要：
This is the sixth, concluding part of a series of papers the first five of which have been submitted to the present archive in mid 1998 and published as INR preprints in 1999. The present paper was printed as an INR preprint, too, but for nonscientific reasons was never made public in any form, electronic or hard-copy. In it I define the bivector derivative for four- and five-vector fields in the case of arbitrary Riemannian geometry; examine a more general case of five-vector affine connection; introduce the five-vector analog of the curvature tensor; and consider a possible five-vector generalization of the Einstein and Kibble-Sciama equations. In conclusion, I define the bivector derivative for the fields of nonspacetime vectors and tensors and derive a possible five-vector generalization of Maxwell's equation.
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