By Luther Pfahler Eisenhart

*Non-Riemannian Geometry*bargains essentially with manifolds ruled by way of the geometry of paths constructed by means of the writer, Luther Pfahler Eisenhart, and Oswald Veblen, who have been college colleagues at Princeton collage in the course of the early 20th century. Eisenhart performed an energetic function in constructing Princeton's preeminence one of the world's facilities for mathematical learn, and he's both well known for his achievements as a researcher and an educator.

In Riemannian geometry, parallelism is set geometrically by means of this estate: alongside a geodesic, vectors are parallel in the event that they make a similar attitude with the tangents. In non-Riemannian geometry, the Levi-Civita parallelism imposed

*a priori*is changed by means of a decision via arbitrary capabilities (affine connections). during this quantity, Eisenhart investigates the most effects of the deviation.

Starting with a attention of uneven connections, the writer proceeds to a contrasting survey of symmetric connections. Discussions of the projective geometry of paths keep on with, and the ultimate bankruptcy explores the geometry of sub-spaces.