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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.
Elementary differential geometry of plane curves. Cambridge tracts in mathematics and mathematical physics .. ;No. 20. Cambridge University Press. 1920. [9] Dover reprint. 2005. Statistical mechanics, the theory of the properties of matter in equilibrium; based on an essay awarded the Adams prize in the University of Cambridge, 1923–24 ...
He is known for contributions to differential geometry, including two widely-used textbooks on its foundational theory. [2] He was the author of eighteen research articles, the last of which was published in 1973. He received his Ph.D. in mathematics in 1951 from the Massachusetts Institute of Technology. His doctoral advisor was Witold Hurewicz.
In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor.
The differential-geometric properties of a parametric curve (such as its length, its Frenet frame, and its generalized curvature) are invariant under reparametrization and therefore properties of the equivalence class itself. The equivalence classes are called C r-curves and are central objects studied in the differential geometry of curves.
Download as PDF; Printable version; ... is a major result of differential geometry, ... Elementary Differential Geometry. New York: Academic Press. pp. 271–275.
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]
In differential geometry, Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least . Equivalently, the average curvature is at least 2 π / L {\displaystyle 2\pi /L} , where L {\displaystyle L} is the length of the curve.
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