Mixed metric 3-contact manifolds and paraquaternionic K\"ahler manifolds

TL;DR

This paper investigates manifolds with mixed metric 3-contact structures, demonstrating their integrability, constant curvature properties, and their relation to paraquaternionic K"ahler manifolds, revealing new geometric insights.

Contribution

It establishes the integrability and curvature properties of mixed metric 3-contact manifolds and links these structures to paraquaternionic K"ahler geometry, providing new theoretical connections.

Findings

Distribution spanned by Reeb vector fields is integrable.

Integral manifolds are totally geodesic with constant sectional curvature.

Structures project onto paraquaternionic K"ahler manifolds.

Abstract

We study manifolds endowed with mixed metric 3--contact structures, proving that the distribution spanned by the Reeb vector fields is integrable, with totally geodesic integral manifolds, of constant sectional curvature $k=\pm1$. We also prove a result of projectability of such structures onto paraquaternionic K\"ahlerian structures.