Cohomological tautness for Riemannian foliations

TL;DR

This paper explores cohomological criteria for tautness in Riemannian foliations, extending classical results to include singular foliations on closed manifolds, thus broadening the understanding of their geometric properties.

Contribution

It introduces an extended cohomological characterization of tautness applicable to singular Riemannian foliations on closed manifolds, generalizing previous results.

Findings

Cohomological characterization of tautness for Riemannian foliations.

Extension of tautness criteria to singular foliations.

Broader understanding of foliation properties on closed manifolds.

Abstract

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold.