Curvature properties of 3-quasi-Sasakian manifolds

TL;DR

This paper investigates the curvature characteristics of 3-quasi-Sasakian manifolds, revealing conditions under which they resemble Sasakian manifolds and classifying those with constant horizontal sectional curvature.

Contribution

It establishes new curvature identities for 3-quasi-Sasakian manifolds and characterizes those with constant horizontal sectional curvature as either 3-1-Sasakian or 3-cosymplectic.

Findings

Derived curvature properties similar to Sasakian identities.

Proved that constant horizontal sectional curvature implies 3-1-Sasakian or 3-cosymplectic structure.

Abstract

We find some curvature properties of 3-quasi-Sasakian manifolds which are similar to some well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional curvature is necessarily either 3-\alpha-Sasakian or 3-cosymplectic.