Eisenhart, Luther Pfahler (1876-1965)

US theoretical geometrist who formulated a unifying principle to the theory of the deformation of surfaces. In the 1920s he attempted to develop his own geometry theory from that of German mathematician Georg Riemann. Eisenhart was born in York, Pennsylvania, and studied at Gettysburg College, Pennsylvania, and Johns Hopkins University, Baltimore. His life's work in mathematical research was spent at Princeton University 1900-45. One of Eisenhart's major achievements was to relate his theories regarding differential geometry to studies bordering on the topological. At the age of 25 he wrote one of the first characterizations of a sphere as defined in terms of differential geometry (the paper had the somewhat daunting title 'Surfaces whose first and second forms are respectively the second and first forms of another surface'). The deformation of a surface involves the congruence of lines connecting a point and its image. Eisenhart's contribution was to realize that, in all known cases, the intersections of these surfaces with the given surface and its image form a set of curves which have special properties. He wrote his account of the theory in 1923, in Transformations of Surface.