Topic
Riemann curvature tensor
About: Riemann curvature tensor is a research topic. Over the lifetime, 6248 publications have been published within this topic receiving 138871 citations. The topic is also known as: Riemann–Christoffel tensor.
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TL;DR: In this article, the Camassa-Holm equation is shown to give rise to a geodesic flow of a certain right invariant metric on the Bott-Virasoro group.
483 citations
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01 Jan 1950
TL;DR: In this article, the Unconnected Manifold and the affinely connected manifold are discussed, and the meaning of the metric according to the special theory of relativity is discussed.
Abstract: Introduction Part I. The Unconnected Manifold: 1. Invariance 2. Integrals Part II. Affinely Connected Manifold: 3. Invariant derivatives 4. Some relations between ordinary and invariant derivatives 5. The notion of parallel transfer 6. The curvature tensor 7. The geodesics of an affine connexion 8. The general geometrical hypothesis about gravitation Part III. Metrically Connected Manifold: 9. Metrical affinities 10. The meaning of the metric according to the special theory of relativity 11. Conservation laws and variational principles 12. Generalizations of Einstein's theory.
478 citations
TL;DR: In this paper, it was shown that in certain compactifications of Minkowski space-time theory on eight-manifolds, the four-form field strength can have a non-vanishing expectation value, while an $N=2$ supersymmetry is preserved.
Abstract: We show that in certain compactifications of ${\cal M}$-theory on eight-manifolds to three-dimensional Minkowski space-time the four-form field strength can have a non-vanishing expectation value, while an $N=2$ supersymmetry is preserved. For these compactifications a warp factor for the metric has to be taken into account. This warp factor is non-trivial in three space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi identity. While the original metric on the internal space is not K\"ahler, it can be conformally transformed to a metric that is K\"ahler and Ricci flat, so that the internal manifold has $SU(4)$ holonomy.
466 citations
TL;DR: In this article, the entropy of extremal black holes arising from terms quadratic in the Riemann tensor in N = 2, D = 4 supergravity theories was determined.
459 citations
01 Jan 2016
TL;DR: The metric spaces of non positive curvature is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
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446 citations