Riemannian foliations with parallel or harmonic basic forms

2013/10/30 by Chami, Fida EL, Habib, Georges, Nakad, Roger
#53C12 #53C20 #53C24 #57R30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.8060

Abstract

In this paper, we consider a Riemannian foliation whose normal bundle carries a parallel or harmonic basic form. We estimate the norm of the O'Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

Related

• Vanishing theorems of the basic harmonic forms on a complete foliated Riemannian manifold
• Riemannian foliations of bounded geometry
• Local canonical foliations of Lorentzian manifolds with bounded curvature
• Orthogonal foliations on riemannian manifolds
• The basic component of the mean curvature of Riemannian foliations