对偶映射与度量扩张
Duality Mappings and Metric Extensor
摘要：
我们引入了对偶映射和度量扩张子的关键概念。给出了包含对偶映射的基本恒等式，并揭示了度量张量与度量扩张量之间的逻辑等价性。利用对偶映射和度量扩张子，我们构造了所谓的度量积，即，多向量和多形式的标量积和压缩积。得到了度量积的恒等式。我们发现的基本公式涉及度量扩张，特别是，我们尝试了令人惊讶的反演公式。这一提议一劳永逸地揭示了公制产品的一个意想不到的含义。
英文摘要：
We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric extensor. By making use of the duality mappings and the metric extensor, we construct the so-called metric products, i.e., scalar product and contracted products of both multivectors and multiforms. The so-known identities involving the metric products are obtained. We find the fundamental formulas involving the metric extensor and, specially, we try its surprising inversion formula. This proposal unveils, once and for all, an unsuspected meaning of the metric products.
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