Riemannian Geometry

In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry. He begins with tensor analysis, including the Riemann curvature tensor, the Christoffel symbols, and the Ricci tensor. From here the notion of a metric is introduced, and hence geodesics, parallel displacement, and the Bianchi identity are explored. Other topics include orthogonal ennuples, the geometry of subspaces, subspaces of a flat space, and groups of motions. This clear and concise guide to Riemannian geometry will be of great interest to mathematicians and theoretical physicists alike.