# Twistorial examples of Riemannian almost product manifolds and their Gil-Medrano and Naveira types

## TL;DR

This paper constructs non-trivial Riemannian almost product structures on twistor spaces of four-manifolds, classifies their types, and provides geometric interpretations of these classes.

## Contribution

It introduces new examples of Riemannian almost product structures on twistor spaces and analyzes their Gil-Medrano and Naveira types with geometric insights.

## Key findings

- Structures are constructed on product bundles of twistor spaces.
- The types of these structures are classified and interpreted geometrically.
- Provides explicit examples and classifications of almost product structures.

## Abstract

Non-trivial examples of Riemannian almost product structures are constructed on the product bundle of the positive and negative twistor spaces of an oriented Riemannian four-manifold. The Gil-Medrano and Naveira types of these structures are determined and a geometric interpretation of the corresponding classes is given.