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A brief note on the spectrum of the basic Dirac operator
In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We thenExpand
Some remarks on Calabi-Yau and hyper-K\"ahler foliations
We study Riemannian foliations whose transverse Levi-Civita connection $\nabla$ has special holonomy. In particular, we focus on the case where $Hol(\nabla)$ is contained either in SU(n) or in Sp(n).Expand
A new upper bound for the Dirac operator on hypersurfaces
We prove a new upper bound for the first eigenvalue of the Dirac operator of a compact hypersurface in any Riemannian spin manifold carrying a non-trivial twistor spinor without zeros on theExpand
Essential norm of Cesàro operators on Lp and Cesàro spaces
Abstract In this paper, we consider the Cesaro-mean operator Γ acting on some Banach spaces of measurable functions on ( 0 , 1 ) , as well as its discrete version on some sequences spaces. We computeExpand
Given a smooth foliation on a closed manifold, basic forms are differential forms that can be expressed locally in terms of the transverse variables. The space of basic forms yields a differentialExpand
Skew Killing spinors in four dimensions
This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor ψ is a spinor that satisfies the equation ∇Xψ = AX · ψ withExpand
Homotopy invariance of cohomology and signature of a Riemannian foliation
We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant.Expand
Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary
On a compact Riemannian manifold whose boundary is endowed with a Riemannian flow, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic 1-forms. The equalityExpand
Geometric aspects of transversal Killing spinors on Riemannian flows
We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those flows carrying non-trivial solutions.
A spectral estimate for the Dirac operator on Riemannian flows
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensionalExpand