# The spectral sequence of the canonical foliation on Vaisman manifolds

## TL;DR

This paper studies the spectral sequence of a natural foliation on Vaisman manifolds, establishing cohomological bounds and obstructions, and analyzing specific cases and examples.

## Contribution

It introduces a lower bound for spectral sequence terms on Vaisman manifolds and identifies cohomological obstructions for certain foliations.

## Key findings

- Lower bounds for spectral sequence dimensions are established.
- Cohomological obstructions prevent some foliations from being Vaisman-induced.
- Quasi-regular foliations realize the lower bounds.

## Abstract

In this paper we investigate the spectral sequence associated to a Riemannian foliation which arises naturally on a Vaisman manifold. Using the Betti numbers of the underlying manifold we establish a lower bound for the dimension of some terms of this cohomological object. This way we obtain cohomological obstructions for two-dimensional foliations to be induced from a Vaisman structure. We show that if the foliation is quasi-regular the lower bound is realized. In the final part of the paper we discuss two examples.