英语词汇“riemann curvature”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

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.

ΘΚΠ

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.

单词	riemann curvature
释义	> as lemmas Riemann 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. ΘΚΠ 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. extracted from curvaturen. Riemann curvature Riemann curvature n. a mathematical generalization of the concept of curvature to spaces of more than three dimensions.extracted from Riemannn. < as lemmas
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