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
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