A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

Fabrice Baudoin; Erlend Grong; Gianmarco Vega-Molino

doi:10.1007/s10455-022-09827-3

A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

Fabrice Baudoin, Erlend Grong^*, Gianmarco Vega-Molino

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).

Original language	English
Journal	Annals of Global Analysis and Geometry
Volume	61
Issue	4
Pages (from-to)	759-776
Number of pages	18
ISSN	0232-704X
DOIs	https://doi.org/10.1007/s10455-022-09827-3
Publication status	Published - Jun 2022
Externally published	Yes

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title = "A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations",

abstract = "Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).",

author = "Fabrice Baudoin and Erlend Grong and Gianmarco Vega-Molino",

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year = "2022",

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T1 - A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

AU - Baudoin, Fabrice

AU - Grong, Erlend

AU - Vega-Molino, Gianmarco

PY - 2022/6

Y1 - 2022/6

N2 - Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).

AB - Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).

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U2 - 10.1007/s10455-022-09827-3

DO - 10.1007/s10455-022-09827-3

M3 - Journal article

AN - SCOPUS:85124030451

SN - 0232-704X

VL - 61

SP - 759

EP - 776

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 4

ER -

A horizontal Chern–Gauss–Bonnet formula on totally geodesic foliations

Abstract

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