Mixed 3-Sasakian structures and curvature

TL;DR

This paper investigates the curvature properties of mixed 3-Sasakian structures, showing they are Einstein manifolds, and establishes their equivalence with mixed metric 3-contact structures.

Contribution

It proves that manifolds with mixed 3-Sasakian structures are Einstein and demonstrates the equivalence between mixed 3-Sasakian and mixed metric 3-contact structures.

Findings

Manifolds with mixed 3-Sasakian structures are Einstein.

Equivalence established between mixed 3-Sasakian and mixed metric 3-contact structures.

Abstract

In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the identity between the class of mixed 3-Sasakian structures and the class of mixed metric 3-contact structures.