Foliated positive scalar curvature
Webpositive scalar curvature. In this paper, we extend the Gromov–Lawson result as follows. Theorem 1.7 If M is an enlargeable manifold, then no spin foliation of M with Hausdorff … WebMar 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 …
Foliated positive scalar curvature
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WebEnter the email address you signed up with and we'll email you a reset link. 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...
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 … Web2. Variation of total scalar curvature 6 3. Conformal geometry 7 4. Manifolds with negative scalar curvature 8 5. How about R>0? 12 Chapter 2. The positive mass theorem 13 1. Manifolds admitting metrics with positive scalar curvature 13 2. Positive mass theorem: rst reduction 14 3. Minimal slicing 21 4. Homogeneous minimal slicings 38 5.
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 … WebTheorem 1.6 ([GL83]). An enlargeable spin manifold does not admit any metric of positive scalar curvature. In this paper, we extend the Gromov-Lawson result as follows. …
WebKey words: enlargeability, positive scalar curvature, foliations. 1 f2 MOULAY-TAHAR BENAMEUR AND J. L. HEITSCH OCTOBER 24, 2024 This theorem and its generalizations have important and deep consequences. Some of the most far reaching were obtained by Connes and by Gromov and Lawson. ipr productshttp://homepages.math.uic.edu/%7Eheitsch/Foliations&PSC.pdf ipr presseagenturWebJul 23, 2024 · In a recent paper, the authors proved that no spin foliation on a compact enlargeable manifold with Hausdorff homotopy graph admits a metric of positive scalar … ipr proformaWebISBN: 978-981-124-935-8 (hardcover) USD 388.00. ISBN: 978-981-124-937-2 (ebook) USD 310.00. Description. Authors. Volume I contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2024 at IHES. There is some background given. orc 4906.01Webprohibit positive scalar curvature cannot be given solely in terms of the fundamental group. We also use Theorem 1 to investigate the structure of R.+ (M), the space of positive scalar curvature metrics on a manifold M. To do this we need the following. THEOREM 3. Let K be a codimension q > 3 subcomplex of a Riemannian ipr practitioner indiaWebGlobal 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 … ipr proceedingsWebMINIMAL 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, orc 4923.01