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An affine flat structure on M is a sheaf T f of vector spaces that pointwisely span TM the tangent bundle and the tangent bracket of pairs of its sections vanishes. As a local example consider the coordinate vectorfields over a chart of M. A manifold admits an affine flat structure if one can glue together such vectorfields for a covering ...
The Ineos 1:59 Challenge, held on 12 October 2019, was an attempt by Kenyan athlete Eliud Kipchoge to break the two-hour mark for running the marathon distance, which he achieved in a time of 1:59:40.2. The event was specifically created for Kipchoge and held in Vienna, Austria to help market the Nike ZoomX Vaporfly 4%. [1]
Nike, Inc. [note 1] (stylized as NIKE) is an American athletic footwear and apparel corporation headquartered near Beaverton, Oregon, United States. [6] It is the world's largest supplier of athletic shoes and apparel and a major manufacturer of sports equipment, with revenue in excess of US$46 billion in its fiscal year 2022.
These are all groups acting freely and properly discontinuously on , and so the various coset spaces / all naturally have the structure of two-dimensional complete flat Riemannian manifolds. None of them are isometric to one another, and any smooth two-dimensional complete flat connected Riemannian manifold is isometric to one of them.
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A conformal metric is conformally flat if there is a metric representing it that is flat, in the usual sense that the Riemann curvature tensor vanishes. It may only be possible to find a metric in the conformal class that is flat in an open neighborhood of each point.
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