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Positive scalar curvature on foliations: The noncompact case.
- Source :
-
Advances in Mathematics . Dec2022:Part A, Vol. 410, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- Let (M , g T M) be a noncompact (not necessarily complete) enlargeable Riemannian manifold in the sense of Gromov-Lawson and F an integrable subbundle of TM. Let k F be the leafwise scalar curvature associated to g F = g T M | F. We show that if either TM or F is spin, then inf (k F) ≤ 0. This generalizes the famous result of Gromov-Lawson on enlargeable manifolds to the case of foliations. It also extends an ansatz of Gromov on hyper-Euclidean spaces to general enlargeable Riemannian manifolds, as well as recent results on compact enlargeable foliated manifolds due to Benameur-Heitsch et al. to the noncompact situation. [ABSTRACT FROM AUTHOR]
- Subjects :
- *RIEMANNIAN manifolds
*CURVATURE
*FOLIATIONS (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 410
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 160043699
- Full Text :
- https://doi.org/10.1016/j.aim.2022.108699