This mathematics-related article is a stub.
You can help Wikipedia by expanding it.In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold that is induced from the metric tensor on a manifold into which the submanifold is embedded, through the pullback.
[1] It may be determined using the following formula (using the Einstein summation convention), which is the component form of the pullback operation:[2] Here
describe the indices of coordinates
of the submanifold while the functions
μ
encode the embedding into the higher-dimensional manifold whose tangent indices are denoted
Let be a map from the domain of the curve
τ
into the Euclidean manifold
a b cos ( n ⋅ τ ) +
( n ⋅ τ ) +
τ ⊗
τ