New metric structures on g-foliations

In the paper we introduce new metric structures on g-foliations that are less rigid than the well-known structures: almost contact and 3-Sasakian structures as well as f-structures with parallelizable kernel and almost para-ϕ-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 g-foliation, we build deformation retraction of our structures with positive partial Ricci curvature onto the subspace of the aforementioned classical structures.