Eigenvalue Estimate for the basic Laplacian on manifolds with foliated\n boundary, part II

2016/04/08 by Fida El Chami, Georges Habib, Chami, Fida El +5 · 1 citation
Computer Science · Mathematics · #53C12 #53C24 #58J32 #58J50 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1604.02304

openalex publication_date 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [4], we gave a sharp lower bound for the first eigenvalue of the basic\nLaplacian acting on basic 1-forms defined on a compact manifold whose\nboundary is endowed with a Riemannian flow. In this paper, we extend this\nresult to the case of the first eigenvalue on basic p-forms for p>1. As in\n[4], the limiting case allows to characterize the manifold \ℝ \×\nB' / \Γ for some group \Γ, and where B' denotes the unit closed\nball. In particular, we describe the Riemannian product mathbbS¹\×\n mathbbSⁿ as the boundary of a manifold.\n

Citations

• Conformal Killing forms on Riemannian manifolds

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