An Introduction to Differential Geometry with Use of the Tensor Calculus

Abstract

THIS book gives a thorough introductory study of the properties of ordinary points in the differential geometry of curves and surfaces in 3-space. Chapter 1 gives an account of twisted curves, Chapter 2 describes the tensor calculus. In Chapter 3 this calculus is applied to investigate the intrinsic geometry of a surface, that is to say, those properties which depend on the first fundamental form. Chapter 4 develops those properties which derive also from the second fundamental form and therefore characterize the surface as viewed from the enveloping space. An Introduction to Differential Geometry with Use of the Tensor Calculus By Prof. Luther Pfahler Eisenhart. (Princeton Mathematical Series, 3.) Pp. x + 304. (Princeton, N. J.: Princeton University Press; London: Oxford University Press, 1940.) 21s. 6d. net.