# Consider the holonomic basis defined in Box 26.1 . Using that the tangent vector for a curve

## Question:

Consider the holonomic basis defined in Box 26.1 . Using that the tangent vector for a curve can be written \(t=t^{\mu} e_{\mu}=\left(d x^{\mu} / d \lambda\right) e_{\mu}\), show that

Thus, \(g_{\mu v}=e_{\mu}(x) \cdot e_{v}(x)\) and the components of the metric tensor are defined by the scalar products of the coordinate-dependent basis vectors. \(* * *\)

Fantastic news! We've Found the answer you've been seeking!

## Step by Step Answer:

**Related Book For**

## Symmetry Broken Symmetry And Topology In Modern Physics A First Course

**ISBN:** 9781316518618

1st Edition

**Authors:** Mike Guidry, Yang Sun