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Luther Eisenhart was a student at Gettysburg College from 1892 until 1896, receiving his A.B. in 1826. After teaching in a school for a year he undertook graduate study at Johns Hopkins University. He obtained a doctorate in 1900 for a thesis entitled Infinitesimal deformations of surfaces. This work was heavily influenced by Darboux's treatise on the subject and he received little supervision for his doctorate.
Eisenhart spent most of his career at Princeton where he became an instructor in mathematics in 1900. He was promoted to professor in 1909 and worked there until he retired in 1945. He served as Dean of the Faculty from 1925 to 1933 when he became Dean of the Graduate School.
There are two stages in Eisenhart's work although it is all in differential geometry. The first stage continued his doctoral work studying deformations of surfaces. His first book A Treatise in the Differential Geometry of Curves and Surfaces , published in 1909, was on this topic and was a development of courses he had given at Princeton for several years. In [2] this book is described as:
... in textbook form, with numerous problems, introducing the student to classical and modern methods. One of the most interesting novelties of the volume was the socalled 'moving trihedrals' for twisted curves as well as surfaces so freely used in writings of Darboux and others. From the first, methods of the theory of functions of a real variable are employed. The work was of great value in introducing the American student to an important field by the most modern method of the time.The second stage started after 1921 when Eisenhart, prompted by Einstein's general theory of relativity and the related geometries, studied generalisations of Riemannian geometry. He published Riemannian Geometry in 1926 and NonRiemannian Geometry in 1927. The scene is set for the first of these works in [5]:
Riemann proposed the generalisation of the theory of surfaces as developed by Gauss, to spaces of any order, and introduced certain fundamental ideas in this general theory. Important contributions to it were made by Bianchi, Beltrami, Christoffel, Schur, Voss, and others, and RicciCurbastro coordinated and extended the theory with the use of tensor analysis and his absolute calculus. The book gave a presentation of the existing theory of Riemannian geometry after a period of considerable study and development of the subject by LeviCivita, Eisenhart, and many others.In 1933 Eisenhart published Continuous Groups of Transformations which continues the work of his earlier books looking at Lie's theory using the methods of the tensor calculus and differential geometry. Again quoting [5]:
The study of continuous groups of transformations inaugurated by Lie resulted in the developments by Engel, Killing, Scheffers, Schur, Cartan, Bianchi and Fubini, a chapter which closed about the turn of the century. The new chapter began about 1920 with the extended studies of tensor analysis, Riemannian geometry and its generalizations, and the application of the theory of continuous groups to the new physical theories. Eisenhart has thus developed a remarkable body of original material and has notably served his colleagues by frequent surveys of fields in which he had become a specialist.Eisenhart had a long association with the American Mathematical Society being VicePresident in 1914, Colloquium lecturer in 1925 when he lectured on nonRiemannian geometry, he edited the Transactions of the American Mathematical Society from 1917 to 1923, being managing editor in 192023, and was President from 1931 to 1932.
References (4 books/articles)
References elsewhere in this archive:
L P Eisenhart was the President of the American Mathematical Society in 1931  1932. You can see a history of the AMS and a list of AMS presidents.
He was the American Mathematical Society Colloquium Lecturer in 1925. You can see a history of the AMS Colloquium and a list of the lecturers.