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"Non-Riemannian Geometry" is a seminal work in the field of differential geometry, providing a rigorous exploration of the mathematical structures that extend beyond the classical Riemannian framework. Authored by the distinguished mathematician Luther Pfahler Eisenhart, this volume focuses on the theory of affine connections and the geometric properties of manifolds that do not necessarily possess a metric tensor. The work delves into the fundamental concepts of parallelism, geodesics, and curvature, offering a comprehensive treatment of the displacement of vectors and the general theory of linear connections.
Through systematic analysis, Eisenhart examines the relationship between geometry and tensor calculus, establishing a foundation that has proven essential for both theoretical mathematics and the development of general relativity in physics. The text addresses the geometry of paths and the structural implications of asymmetric connections, making it a vital resource for scholars and advanced students interested in the evolution of geometric thought. "Non-Riemannian Geometry" remains a cornerstone of mathematical literature, illustrating the elegant complexity of spaces where the traditional constraints of distance and angle are redefined through broader algebraic and analytical lenses.
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