# A Bonnet-Myers type theorem for quaternionic contact structures

## TL;DR

This paper establishes a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension greater than 7, linking Ricci-type bounds to compactness and diameter bounds in the sub-Riemannian setting.

## Contribution

It extends classical Bonnet-Myers results to higher-dimensional quaternionic contact manifolds with new curvature bounds involving third-order derivatives.

## Key findings

- Manifolds are compact under specified conditions.
- Provides a sharp bound on sub-Riemannian diameter.
- Establishes criteria for compactness in quaternionic contact geometry.

## Abstract

We prove a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms of derivatives up to the third order of the fundamental tensors, then the manifold is compact and we give a sharp bound on its sub-Riemannian diameter.