Relates sectional curvature of a Riemannian manifold to the rate geodesics spread apart
In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch, who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread.
The statement of the theorem involves two Riemannian manifolds, and allows to compare the infinitesimal rate at which geodesics spread apart in the two manifolds, provided that their curvature can be compared. Most of the time, one of the two manifolds is a "comparison model", generally a manifold with constant curvature, and the second one is the manifold under study : a bound (either lower or upper) on its sectional curvature is then needed in order to apply Rauch comparison theorem.
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In Riemannian geometry, the Rauchcomparisontheorem, named after Harry Rauch, who proved it in 1951, is a fundamental result which relates the sectional...
as the sphere theorem for Riemannian manifolds. The Rauchcomparisontheorem is also named after Harry Rauch. He proved it in 1951. Rauch, H. E. (1951)...
manifolds, Jacobi fields, the Morse index, the Rauchcomparisontheorems, and the Cartan–Hadamard theorem. Then it ascends to complex manifolds, Kähler...
2307/2373064. JSTOR 2373064. Warner, F. W. (1966). "Extension of the RauchComparisonTheorem to Submanifolds". Transactions of the American Mathematical Society...
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"Kalman Smoothing". There are several smoothing algorithms in common use. The Rauch–Tung–Striebel (RTS) smoother is an efficient two-pass algorithm for fixed...
– director of communications Sam Seager – head of visual content Lauren Rauch – management coordinator Lauren Evans – physiotherapist Valeska Voiges –...
44(2)::155-9, 2016; PMID 26697726 Veilleux LN, Robert M, Ballaz L, Lemay M, Rauch F: Gait analysis using a force-measuring gangway: Intrasession repeatability...
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