In mathematics and theoretical physics, the induced metric is the metric tensor defined on a submanifold which is calculated from the metric tensor on a larger manifold into which the submanifold is embedded. It may be calculated using the following formula (written using Einstein summation convention):
Here describe the indices of coordinates of the submanifold while the functions encode the embedding into the higher-dimensional manifold whose tangent indices are denoted .
Read more about Induced Metric: Example - Curve On A Torus
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