Modified differentials and basic cohomology for Riemannian foliations

DOI10.1007/s12220-011-9289-6zbMath1276.53031arXiv1007.2955OpenAlexW1992194679WikidataQ115376881 ScholiaQ115376881MaRDI QIDQ363215

Georges Habib, Ken V. Richardson

Publication date: 2 September 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.2955

zbMATH Keywords

Riemannian foliationeigenvalue estimatePoincaré dualitybasic cohomology, basic Laplaciantransverse geometry

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Foliations (differential geometric aspects) (53C12) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (13)

The Bochner formula for Riemannian flows ⋮ Basic Morse-Novikov cohomology for foliations ⋮ Twisted basic Dolbeault cohomology on transverse Kähler foliations ⋮ Twisted Frölicher-type inequality on foliations ⋮ Morse-Novikov cohomology on foliated manifolds ⋮ Basic Dolbeault cohomology and Weitzenböck formulas on transversely Kähler foliations ⋮ The mean curvature of transverse Kähler foliations ⋮ Homotopy invariance of cohomology and signature of a Riemannian foliation ⋮ On Lorentzian manifolds with highest first Betti number ⋮ The \(S^1\)-equivariant signature for semi-free actions as an index formula ⋮ Transverse Weitzenböck formulas and de Rham cohomology of totally geodesic foliations ⋮ PERTURBATIONS OF BASIC DIRAC OPERATORS ON RIEMANNIAN FOLIATIONS ⋮ Some remarks on Calabi-Yau and hyper-Kähler foliations

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