Riemannian foliations with parallel or harmonic basic forms

Fida El Chami, Georges Habib, and Roger Nakad

Address:
F. EL Chami, Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn, Lebanon,
G. Habib, Lebanese University, Faculty of Sciences II, Department of Mathematics, P.O. Box 90656 Fanar-Matn, Lebanon,
R. Nakad, Notre Dame University-Louaizé, Faculty of Natural and Applied Sciences, Department of Mathematics and Statistics, P.O. Box 72, Zouk Mikael, Lebanon,

E-mail:
fchami@ul.edu.lb
ghabib@ul.edu.lb
rnakad@ndu.edu.lb

Abstract: In this paper, we consider a Riemannian foliation that admits a nontrivial 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.

AMSclassification: primary 53C12; secondary 53C20, 53C24, 57R30.

Keywords: Riemannian foliation, parallel and harmonic basic forms, O’Neill tensor.

DOI: 10.5817/AM2015-1-51