TensorFlux.jl

Differential geometry with mathematical notation in Julia

Surfaces

A differential form, also called a p-form, is an antisymmetric (0, p)-tensor. Covectors only have one index, so all covectors are 1-forms. But not all (0, 2)-tensors are 2-forms, only the antisymmetric ones.

julia


                julia> α = Tensor([1, -2]')
                julia> β = Tensor([3, 1]')
                julia> γ = α ∧ β # An asymmetric (0, 2)-tensor, i.e. 2-form
                (0, 2)-Tensor:
                [0.0 7.0; -7.0 0.0]
                    (:co, :co)
                julia> ζ = β ∧ α # Equal to -α ∧ β
                (0, 2)-Tensor:
                [0.0 -7.0; 7.0 0.0]
                    (:co, :co)