A note on transverse divergence and taut Riemannian foliations
arXiv:1411.7214 · doi:10.1016/j.geomphys.2015.06.012
Abstract
In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward consequence. In the final part of the paper we obtain a tautness characterization for transversally oriented foliations with dense leaves and investigate the case of a submanifold of lower dimension which is closed and orthogonal to the leaves.
13 pages, as accepted for publication in J Geom Phys