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These efforts, along with those of Forster, involved making the metric tensor (which had previously been assumed to be symmetric and real-valued) into an asymmetric and/or complex-valued tensor, and they also attempted to create a field theory for matter as well.
In a Riemannian manifold M with metric tensor g, the length of a continuously differentiable curve γ : a,b → M is defined by
The new scalar field comes from a component of the metric tensor where the figure 5 labels an additional, fifth dimension.