Positive scalar curvature on foliations
By Weiping Zhang. 2015
52 citations recorded by the source corpus.
We generalize classical theorems due to Lichnerowicz and Hitchin on the existence of Riemannian metrics of positive scalar curvature on spin manifolds to the case of foliated spin manifolds. As a consequence, we show that there is no foliation of positive leafwise scalar curvature on any torus, which generalizes the famous theorem of Schoen-Yau and Gromov-Lawson on the non-existence of metrics of positive scalar curvature on torus to the case of foliations. Moreover, our method, which is partly inspired by the analytic localization techniques of Bismut-Lebeau, also applies to give a new proof of the celebrated Connes vanishing theorem without using noncommutative geometry.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/82729c4520700d5fe7174b03dc926bfe973c9a5a
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In Applied Mathematics
In Geometry and Topology
- Misha Gromov
- Assaf Naor
- Yann Ollivier
- Alexander Lubotzky
- Damian Osajda
- Denis V. Osin
- Richard Bamler
- Larry Guth
In Mathematical Physics
- Misha Gromov
- Assaf Naor
- Yann Ollivier
- Alexander Lubotzky
- Damian Osajda
- Richard Bamler
- Denis V. Osin
- Larry Guth
Citations in the corpus
- Four Lectures on Scalar Curvature (2019, background): “4 of [Zhang 2016], where it is required that e⊥/eS is large, since the shape of the compact domain in P where the scalar curvature of the metric g̃eS,e⊥ becomes ε-close to that of g, depends on the ratio e⊥/eS , (see section 6.”