Riemannian Geometry

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.

About the author

Luther Pfahler Eisenhart

Summary

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.

Additional text

"Eisenhart's classic work on the application of tensor calculus to geometry was originally published in 1926 . . . It is still one of the best accounts of the subject."---E. J. F. Primrose, Mathematical Gazette

Product details

• Authors: Luther Eisenhart, Luther Pfahler Eisenhart
• Publisher: University Presses
• Languages: English
• Product format: Paperback / Softback
• Released: 02.11.1997
• EAN: 9780691023533
• ISBN: 978-0-691-02353-3
• No. of pages: 272
• Weight: 454 g
• Series: Princeton Landmarks in Mathema; Princeton Landmarks in Mathematics and Physics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Non-fiction book > Nature, technology > Astronomy: general, reference works; SCIENCE / Physics / General, MATHEMATICS / Geometry / Differential, Physics, Differential & Riemannian geometry, Non-Euclidean geometry, Differential and Riemannian geometry, MATHEMATICS / Geometry / Non-Euclidean