Riemannian Manifold has Zero Gaussian Curvature iff Euclidean/Historical Note

Historical Note on Riemannian Manifold has Zero Gaussian Curvature iff Euclidean

Bernhard Riemann demonstrated that a Riemannian Manifold has Zero Gaussian Curvature iff Euclidean in a posthumous paper on heat conduction.

Thus the Riemann-Christoffel tensor measures how much a Riemannian manifold deviates from a Euclidean space.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.32$: Riemann ($\text {1826}$ – $\text {1866}$)