WebJul 14, 2024 · Rauch [ 21] showed that a compact, simply connected Riemannian manifold which is strictly (3 / 4)-pinched is a topological sphere. This raised the question of whether a compact, simply connected manifold whose sectional curvatures all lie in the interval \ ( (\frac {1} {4}, 1]\) is necessarily homeomorphic to the sphere. WebNov 18, 2008 · The differential 1/4-pinched sphere theorem states that if a simply connected compact Riemannian manifold has all its sectional curvatures pinched strictly between 1 …
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WebJun 7, 2000 · simply-connected '-pinched Riemannian manifold. There are several results supporting this conjecture (e.g., [Am], [Ho], [HW1], [Ok]). Here we also give a partial … WebAn analogous Bonnet-Myers theorem is obtained for a complete and positively curved n-dimensional (n≥3) Riemannian manifold M n. We prove that if n ≥4 and the curvature … scaled agile framework story estimation
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WebNov 18, 2008 · The differential 1/4-pinched sphere theorem states that if a simply connected compact Riemannian manifold has all its sectional curvatures pinched strictly between 1 and 4 then it is diffeomorphic to a sphere. The statement in the "homeomorphic" case is the classic sphere theorem of Berger and Klingenberg. Brendle and Schoen's proof involves ... Pinched sectional curvature [ edit] Sphere theorem. If M is a simply connected compact n -dimensional Riemannian manifold with sectional curvature strictly pinched between 1/4 and 1 then M is diffeomorphic to a sphere. Cheeger's finiteness theorem. See more Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies See more What follows is an incomplete list of the most classical theorems in Riemannian geometry. The choice is made depending on its importance and elegance of formulation. Most of … See more 1. ^ maths.tcd.ie 2. ^ Kleinert, Hagen (1989). "Gauge Fields in Condensed Matter Vol II": 743–1440. {{cite journal}}: Cite journal requires journal= (help) 3. ^ Kleinert, Hagen (2008). Multivalued Fields in Condensed Matter, Electromagnetism, and Gravitation (PDF). pp. 1–496. See more Riemannian geometry was first put forward in generality by Bernhard Riemann in the 19th century. It deals with a broad range of geometries whose metric properties vary from … See more • Shape of the universe • Basic introduction to the mathematics of curved spacetime • Normal coordinates • Systolic geometry • Riemann–Cartan geometry in Einstein–Cartan theory (motivation) See more • Riemannian geometry by V. A. Toponogov at the Encyclopedia of Mathematics • Weisstein, Eric W. "Riemannian Geometry". MathWorld. See more Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A saxon facility services inc