Project SherlockEst. Knowledge

Book

1909

A Treatise on the Differential Geometry of Curves and Surfaces

Luther Pfahler Eisenhart

Develops the geometry of a surface entirely from its first and second fundamental forms, treating Gauss's Theorema Egregium as the fact that curvature is intrinsic and geodesics as the resulting generalisation of a straight line.

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FreeAdvancedlink checked 17 Sept 2026

Read these first

Not a difficulty warning — a route. These are in the library too.

General Investigations of Curved SurfacesCarl Friedrich Gauss, 1828Proves the Theorema Egregium: a surface's curvature can be measured from within the surface itself, without reference to the space it sits in — which is what makes intrinsic geometry possible.

Groundwork for

Works in the library that name this one as a prerequisite.

Riemannian GeometryLuther Pfahler Eisenhart, 1926Develops the tensor calculus of Riemannian manifolds systematically, giving the curvature and geodesic machinery in the form general relativity had just made indispensable.

Filed under Geometry in Mathematics.