H-type foliations

Fabrice Baudoin; Erlend Grong; Luca Rizzi; Gianmarco Vega-Molino

doi:10.1016/j.difgeo.2022.101952

H-type foliations

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

^*Corresponding author af dette arbejde

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

4 Citationer (Scopus)

Abstract

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K-contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound on these structures, we prove a sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann [38], we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of these spaces in codimension more than 2.

Originalsprog	Engelsk
Artikelnummer	101952
Tidsskrift	Differential Geometry and its Application
Vol/bind	85
ISSN	0926-2245
DOI	https://doi.org/10.1016/j.difgeo.2022.101952
Status	Udgivet - dec. 2022
Udgivet eksternt	Ja

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

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AU - Baudoin, Fabrice

AU - Grong, Erlend

AU - Rizzi, Luca

AU - Vega-Molino, Gianmarco

PY - 2022/12

Y1 - 2022/12

N2 - With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K-contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound on these structures, we prove a sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann [38], we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of these spaces in codimension more than 2.

AB - With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K-contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound on these structures, we prove a sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann [38], we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of these spaces in codimension more than 2.

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U2 - 10.1016/j.difgeo.2022.101952

DO - 10.1016/j.difgeo.2022.101952

M3 - Journal article

AN - SCOPUS:85137794274

SN - 0926-2245

VL - 85

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

M1 - 101952

ER -

H-type foliations

Abstract

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