General Relativity: An Introduction for Physicists · Problem 2.12

Manifolds and coordinates — Hobson, Efstathiou & Lasenby

Physics · embedding-two-dimensional-manifold

Problem

Consider the two-dimensional space with line element

ds^2 = \frac{dr^2}{1-2\mu/r} + r^2\,d\phi^2.

Using the result (2.25), show that this geometry can be embedded in three-dimensional Euclidean space, and find the equations for the corresponding two-dimensional surface.

Related theory

Dimensional Formulae And Dimensional Equations

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