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单词 ricci curvature
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Ricci curvature
b. The degree or manner in which the geometry of a space or manifold (esp. of three of more dimensions) differs from that of Euclidean space; any of several quantities which measure or mathematically characterize this (frequently with distinguishing word, as Riemann curvature, Ricci curvature, etc.); the property or state of being non-Euclidean.The generalization of the notion of curvature to spaces and manifolds originates in the study of non-Euclidean geometry, especially in the work of German mathematician Bernhard Riemann (1826–66). One of the most well known applications of this is found in Einstein's general theory of relativity, where it provides a mathematical framework for describing the curvature of space-time.
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the world > relative properties > number > geometry > geometric space > [noun] > non-Euclidean
hyperspace1867
curvature1873
Riemann space1894
non-Euclidean space1939
1873 Illustr. London News 15 Mar. 255/3 The Professor [sc. W. K. Clifford] described what he considered the nature of things would be on the supposition that the curvature of all space is nearly uniform and positive.
1920 A. S. Eddington Space, Time & Gravitation x. 158 We thus get the idea that space-time may have an essential curvature on a great scale independent of the small hummocks due to recognised matter.
1921 Amer. Jrnl. Math. 43 220 This is recognized as a manifold of constant Riemann curvature.
1966 E. F. Taylor & J. A. Wheeler Spacetime Physics iii. 175 The existence of this curvature destroys the possibility of describing motion with respect to a single ideal Euclidean reference frame that pervades all space.
1986 New Scientist 23 Oct. 55/1 In the notes I provide for students on my course in relativity, the computation of the Ricci curvature from this metric takes four typewritten pages, although the final result is in fact 0.
2013 Proc. Royal Soc. A. 469 2 The underlying space in this case is an infinite-dimensional Kähler manifold with positive (but non-constant) curvature.
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