An Introduction To Differential Geometry With Use Of Tensor Calculus - Eisenhart L P
Since 1909, when my Differential Geometry of Curves and Surfaces was
published, the tensor calculus, which had previously been invented by
Ricci, was adopted by Einstein in his General Theory of Relativity, and
has been developed further in the study of Riemannian Geometry and
various generalizations of the latter. In the present book the tensor
calculus of euclidean 3-space is developed and then generalized so as to
apply to a Riemannian space of any number of dimensions. The tensor
calculus as here developed is applied in Chapters III and IV to the
study of differential geometry of surfaces in 3-space, the material treated
being equivalent to what appears in general in the first eight chapters
of my former book with such additions as follow from the introduction
of the concept of parallelism of Levi-Civita and the content of the tensor
calculus.
Of the many exercises in the book some involve merely direct appli-
cation of the text, but most of them constitute an extension of it.
In the writing of the book I have received valuable assistance and
criticism from Professor H. P. Robertson and from my students, Messrs.
Isaac Battin, Albert J. Coleman, Douglas R. Crosby, John Giese, Donald
C. May, and in particular, Wayne Johnson.
The excellent line drawings and half-tone illustrations were conceived
and executed by Mr. John H. Lewis.
- DJVU: 304 pages
- Publisher: Princeton University Press, 1947
- Language: English
Since 1909, when my Differential Geometry of Curves and Surfaces was
published, the tensor calculus, which had previously been invented by
Ricci, was adopted by Einstein in his General Theory of Relativity, and
has been developed further in the study of Riemannian Geometry and
various generalizations of the latter. In the present book the tensor
calculus of euclidean 3-space is developed and then generalized so as to
apply to a Riemannian space of any number of dimensions. The tensor
calculus as here developed is applied in Chapters III and IV to the
study of differential geometry of surfaces in 3-space, the material treated
being equivalent to what appears in general in the first eight chapters
of my former book with such additions as follow from the introduction
of the concept of parallelism of Levi-Civita and the content of the tensor
calculus.
Of the many exercises in the book some involve merely direct appli-
cation of the text, but most of them constitute an extension of it.
In the writing of the book I have received valuable assistance and
criticism from Professor H. P. Robertson and from my students, Messrs.
Isaac Battin, Albert J. Coleman, Douglas R. Crosby, John Giese, Donald
C. May, and in particular, Wayne Johnson.
The excellent line drawings and half-tone illustrations were conceived
and executed by Mr. John H. Lewis.
