Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations

Fabrice Baudoin; Erlend Grong

doi:10.1007/s10455-019-09672-x

Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

4 Citationer (Scopus)

Abstract

We prove transverse Weitzenböck identities for the horizontal Laplacians of a totally geodesic foliation. As a consequence, we obtain nullity theorems for the de Rham cohomology assuming only the positivity of curvature quantities transverse to the leaves. Those curvature quantities appear in the adiabatic limit of the canonical variation of the metric.

Originalsprog	Engelsk
Tidsskrift	Annals of Global Analysis and Geometry
Vol/bind	56
Nummer	2
Sider (fra-til)	403-428
Antal sider	26
ISSN	0232-704X
DOI	https://doi.org/10.1007/s10455-019-09672-x
Status	Udgivet - sep. 2019
Udgivet eksternt	Ja

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Citationsformater

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abstract = "We prove transverse Weitzenb{\"o}ck identities for the horizontal Laplacians of a totally geodesic foliation. As a consequence, we obtain nullity theorems for the de Rham cohomology assuming only the positivity of curvature quantities transverse to the leaves. Those curvature quantities appear in the adiabatic limit of the canonical variation of the metric.",

keywords = "De Rham cohomology, Sub-Laplacians, Totally geodesic foliation",

author = "Fabrice Baudoin and Erlend Grong",

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T1 - Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations

AU - Baudoin, Fabrice

AU - Grong, Erlend

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AB - We prove transverse Weitzenböck identities for the horizontal Laplacians of a totally geodesic foliation. As a consequence, we obtain nullity theorems for the de Rham cohomology assuming only the positivity of curvature quantities transverse to the leaves. Those curvature quantities appear in the adiabatic limit of the canonical variation of the metric.

KW - De Rham cohomology

KW - Sub-Laplacians

KW - Totally geodesic foliation

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DO - 10.1007/s10455-019-09672-x

M3 - Journal article

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EP - 428

JO - Annals of Global Analysis and Geometry

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Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations

Abstract

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