Foliated positive scalar curvature
WebDec 3, 2024 · Foliations Positive scalar curvature 1. Introduction A classical result of Lichnerowicz [10] states that if a closed spin manifold carries a Riemannian metric of …
Foliated positive scalar curvature
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WebAug 19, 2015 · Positive scalar curvature on foliations. We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar … WebMay 3, 2016 · Positive scalar curvature on foliations By Weiping Zhang Abstract We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of …
Webcannot carry a complete metric of positive scalar curvature. The following result is a foliated extension of Theorem1.7. Theorem 1.8. Let (M;F) be a foliated manifold. If Mis 2-enlargeable along F, then Mcannot carry a complete metric gTM satisfying that kF, the leafwise scalar curvature of gTM along F, is positive everywhere. Webwith Hausdorff homotopy groupoid has a metric of positive scalar curvature. In addition, the techniques used here lead immediately to the following results. We obtain a bound on how large the scalar curvature on a spin foliation with Hausdorff homotopy groupoid can be which is a multiple of a natural extension of Gromov’s K-area of M. See ...
WebMay 30, 2024 · Positive scalar curvature on foliations: the noncompact case. Let be a noncompact enlargeable Riemannian manifold in the sense of Gromov-Lawson and an … WebMay 30, 2024 · Let $k^ {F}$ be the leafwise scalar curvature associated to $g^F=g^ {TM} _F$. We show that if either $TM$ or $F$ is spin, then $ {\rm inf} (k^F)\leq 0$. This generalizes earlier claims for...
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WebPositive scalar curvature on foliations Pages 1035-1068 from Volume 185 (2024), Issue 3 by Weiping Zhang Abstract We generalize classical theorems due to Lichnerowicz and … my little echo shopWebMay 1, 2024 · Positive scalar curvature on foliations May 2024 DOI: Authors: Weiping Zhang Abstract We generalize classical theorems due to Lichnerowicz and Hitchin on the … my little emoWebMar 21, 2024 · Lichnerowicz proved that if M is a closed spin manifold which admits a positive scalar curvature metric, then A ^ ( M) = 0. In dimensions 4 k, α ( M) = 2 A ^ ( M), so it follows that α ( M) = 0. In fact, Hitchin proved that α … my little eco shop ltdWebPositive scalar curvature means balls of radius rfor small rhave a smaller volume than balls of the same radius in Euclidean space; negative scalar curvature means they have larger volume. In the special case n= 2, the scalar curvature is just twice the Gaussian curvature. This paper will deal with bounds on the scalar curvature, and especially ... my little echoWebGlobal Analysis on Foliated Spaces - December 2005. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better … my little earth wingsWebMINIMAL SURFACES AND SCALAR CURVATURE 3 Remark 2. Note the potential confusion in Lemma 1: X is a vector eld on Mthat is not necessarily tangent to (indeed, we will see that the interesting situations are when Xis not tangent to ). So we cannot take the divergence of Xas a vector eld tangent to . We are also not taking the full g-divergence, my little eco companyWebMar 8, 2024 · We extend the deep and important results of Lichnerowicz, Connes, and Gromov-Lawson which relate geometry and characteristic numbers to the existence and … my little empire fashion