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4. Consider Euclidean space in D = 2. Show by direct computation that the Riemann curvature tensor, vanishes in: RA = 0μΓλ,ρ - 0,Γ^μρ + ΓλμσΓσνρ - ΓλνσΓσμο, ρμν ·

4. Consider Euclidean space in D = 2. Show by direct computation that the Riemann curvature tensor, vanishes in: RA = 0μΓλ,ρ - 0,Γ^μρ + ΓλμσΓσνρ - ΓλνσΓσμο, ρμν ·

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Consider Euclidean space in D = 2. Show by direct computation that the Riemann curvature tensor,

vanishes in: rest on image 

4. Consider Euclidean space in D = 2. Show by direct computation that the Riemann curvature tensor, vanishes in: RA pμv = μ¹vp - ₂² up + r² ρμν μρ О,ГА, + ΓλμσΓσνρ - ΓλυσΓσ 00 a) Cartesian coordinates, such that ds² = dx² + dy². b) polar coordinates, such that ds² = dr² + r²d0². You can use the fact that the only non-vanishing Christoffel symbols are = -r, го ro = Го μρη Or
Transcribed Image Text:4. Consider Euclidean space in D = 2. Show by direct computation that the Riemann curvature tensor, vanishes in: RA pμv = μ¹vp - ₂² up + r² ρμν μρ О,ГА, + ΓλμσΓσνρ - ΓλυσΓσ 00 a) Cartesian coordinates, such that ds² = dx² + dy². b) polar coordinates, such that ds² = dr² + r²d0². You can use the fact that the only non-vanishing Christoffel symbols are = -r, го ro = Го μρη Or
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