Static perfect fluid space-time and paracontact metric geometry

Abstract

The main purpose of this paper is to study and explore some characteristics of static perfect fluid space-time on paracontact metric manifolds. First, we show that if a [Formula: see text]-paracontact manifold [Formula: see text] is the spatial factor of a static perfect fluid space-time, then [Formula: see text] is of constant scalar curvature [Formula: see text] and squared norm of the Ricci operator is given by [Formula: see text]. Next, we prove that if a [Formula: see text]-paracontact metric manifold [Formula: see text] with [Formula: see text] is a spatial factor of static perfect space-time, then for [Formula: see text], [Formula: see text] is flat, and for [Formula: see text], [Formula: see text] is locally isometric to the product of a flat [Formula: see text]-dimensional manifold and an [Formula: see text]-dimensional manifold of constant negative curvature [Formula: see text]. Further, we prove that if a paracontact metric 3-manifold [Formula: see text] with [Formula: see text] is a spatial factor of static perfect space-time, then [Formula: see text] is an Einstein manifold. Finally, a suitable example has been constructed to show the existence of static perfect fluid space-time on paracontact metric manifold.