Riemannian Geometry

1950/12/31 by Luther Pfahler Eisenhart · 14 citations
Physics and Astronomy · Medicine · Mathematics · #Relativity and Gravitational Theory #Spaceflight effects on biology #Advanced Differential Geometry Research #Geometry #Riemannian geometry #Mathematics #Physics #Pure mathematics

paper · doi:10.1515/9781400884216

openalex publication_date 1950/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late nineteenth century, as mathematicians such as Riemann increasingly questioned Euclid's parallel postulate, and by relaxing this constraint derived a wealth of new results. These seemingly abstract properties found immediate application in physics upon Einstein's introduction of the general theory of relativity. In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.

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