Synopses & Reviews
Non-Riemannian Geometry deals basically with manifolds dominated by the geometry of paths developed by the author, Luther Pfahler Eisenhart, and Oswald Veblen, who were faculty colleagues at Princeton University during the early twentieth century. Eisenhart played an active role in developing Princeton's preeminence among the world's centers for mathematical study, and he is equally renowned for his achievements as a researcher and an educator.
In Riemannian geometry, parallelism is determined geometrically by this property: along a geodesic, vectors are parallel if they make the same angle with the tangents. In non-Riemannian geometry, the Levi-Civita parallelism imposed a priori is replaced by a determination by arbitrary functions (affine connections). In this volume, Eisenhart investigates the main consequences of the deviation.
Starting with a consideration of asymmetric connections, the author proceeds to a contrasting survey of symmetric connections. Discussions of the projective geometry of paths follow, and the final chapter explores the geometry of sub-spaces.
Synopsis
Non-Riemannian Geometry deals basically with manifolds dominated by the geometry of paths co-developed by the distinguished mathematician Luther Pfahler Eisenhart, the author of this text. He begins with a consideration of asymmetric connections, and then proceeds to a contrasting survey of symmetric connections. Discusses projective geometry of paths and the geometry of sub-spaces. 1927 edition.
Synopsis
Non-Riemannian Geometry deals basically with manifolds dominated by the geometry of paths co-developed by the distinguished mathematician Luther Pfahler Eisenhart, who is also the author of this text. Its concise treatment starts with a consideration of asymmetric connections, after which it proceeds to a contrasting survey of symmetric connections. Discussions of the projective geometry of paths follow; and in the final chapter, Eisenhart explores the geometry of sub-spaces. 1927 ed.
Table of Contents
I. Asymmetric Connections
II. Symmetric Connections
III. Projective Geometry of Paths
IV. The Geometry of Sub-spaces
Bibliography