General Relativity: An Introduction for Physicists · Problem 7.10

The equivalence principle and spacetime curvature — Hobson, Efstathiou & Lasenby

Physics · line-element-flat-vs-curved

Problem

Show that the line element ds2=y2 dx2+x2 dy2ds^2 = y^2\,dx^2 + x^2\,dy^2 represents the Euclidean plane, but the line element ds2=y dx2+x dy2ds^2 = y\,dx^2 + x\,dy^2 represents a curved two-dimensional manifold.

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