# The Partial Ricci Flow on $\mathfrak{g}$-foliations

## TL;DR

This paper introduces new metric structures on $rak{g}$-foliations that are more flexible than classical structures, and uses a partial Ricci flow to deform these structures onto well-known classical ones.

## Contribution

It defines novel metric structures on $rak{g}$-foliations and demonstrates a deformation retraction onto classical structures via a partial Ricci flow.

## Key findings

- New metric structures on $rak{g}$-foliations introduced.
- Deformation retraction onto classical structures established.
- Flow preserves positive partial Ricci curvature.

## Abstract

In the paper we introduce new metric structures on $\mathfrak{g}$-foliations that are less rigid than the well-known structures: almost contact and 3-quasi-Sasakian structures as well as $f$-structures with parallelizable kernel and almost para-$\phi$-structures with complemented frames. We discuss the properties of the new structures in order to demonstrate similarities with the corresponding classical structures. Then using the flow of metrics on a $\mathfrak{g}$-foliation, we build deformation retraction of our structures with positive partial Ricci curvature onto the subspace of the aforementioned classical structures.