# H-type foliations

## TL;DR

This paper introduces H-type foliations as a generalization of K-contact geometries, providing new insights into their curvature properties, eigenvalues, and classification under certain geometric conditions.

## Contribution

It defines H-type foliations, establishes diameter and eigenvalue bounds, classifies those with parallel Clifford structures, and explores their Einstein and Ricci curvature properties.

## Key findings

- Derived sub-Riemannian diameter upper bounds.
- Estimated first eigenvalues of the sub-Laplacian.
- Classified H-type foliations with parallel Clifford structures.

## Abstract

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound, we prove on those structures sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of those spaces in codimension more than 2.