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Calculus on Manifolds is a brief monograph on the theory of vector-valued functions of several real variables (f : R n →R m) and differentiable manifolds in Euclidean space. . In addition to extending the concepts of differentiation (including the inverse and implicit function theorems) and Riemann integration (including Fubini's theorem) to functions of several variables, the book treats ...
His five-volume A Comprehensive Introduction to Differential Geometry [11] is among his most influential and celebrated works. The distinctive pedagogical aim of the work, as stated in its preface, was to elucidate for graduate students the often obscure relationship between classical differential geometry—geometrically intuitive but imprecise—and its modern counterpart, replete with ...
Differential geometry finds applications throughout mathematics and the natural sciences. Most prominently the language of differential geometry was used by Albert Einstein in his theory of general relativity, and subsequently by physicists in the development of quantum field theory and the standard model of particle physics.
See also multivariable calculus, list of multivariable calculus topics. Manifold. Differentiable manifold; Smooth manifold; Banach manifold; Fréchet manifold; Tensor analysis. Tangent vector
In 1901–1902 he published a famous two-volume textbook entitled Anwendung der Differential- und Integralrechnung auf die Geometrie (application of differential and integral calculus to geometry). The first volume subtitled Einführung in die Theorie der Curven in der Ebene und in Raum was published in 1901 and dealt with curves . [ 1 ]
Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.
In 1950 Struik published his Lectures on Classical Differential Geometry, [13] which gained praise from Ian R. Porteous: Of all the textbooks on elementary differential geometry published in the last fifty years the most readable is one of the earliest, namely that by D.J. Struik (1950). He is the only one to mention Allvar Gullstrand. [14]
Kentaro Yano (1 March 1912 in Tokyo, Japan – 25 December 1993) was a mathematician working on differential geometry [2] who introduced the Bochner–Yano theorem. He also published a classical book about geometric objects (i.e., sections of natural fiber bundles ) and Lie derivatives of these objects.