General Relativity
Contents
(1, 1)-tensor t = tij ∂i ⊗ dxj, t(-, v) = tij ∂i ⊗ dxj (vk ∂k) = tij vk ∂i ⊗ dxj (∂k) = tij vk δkj ∂i = tij vj ∂i. g(v, v) = gi, j vi vj = -1. Metric tensor g = gi, j dxi ⊗ dxj. g(-, v) = gi, j dxi ⊗ dxj (vk ∂k) = (gi, j vj) dxi.