Curvature Tensor

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📖Definition

Tensor measuring curvature of manifold. Indicates if space is flat or curved

📐Formulas

Riemann curvature: R^ρ_σμν
Ricci curvature: R_μν = R^ρ_μρν
Scalar curvature: R = g^μνR_μν

✏️Examples

예제 1

Plane: R = 0

예제 2

Sphere: R = 2/r²

예제 3

Hyperboloid: R < 0

Applications

General relativity

Cosmology

Geometry

🔗Related Documents

Applications

#곡률#curvature#리만#Riemann