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^{μ}verses the 2D surface parameterized by (σ,τ). Are x

^{μ}locally Euclidean? Are the coordinates (σ,τ) locally Euclidean? Remember x

^{μ}are functions of the parameters (σ,τ) or x

^{μ}=x

^{μ}(σ,τ) which defines a surface in space-time. How does this all relate to manifold theory?

Thanks.