A Study of Three-Dimensional Paracontact $(\kappa ,\mu ,\nu) $-SPACES

Abstract

This paper is a study of three-dimensional paracontact metric (\k{appa},{\mu},{\nu})-manifolds. Three dimensional paracontact metric manifolds whose Reeb vector field {\xi} is harmonic are characterized. We focus on some curvature properties by considering the class of paracontact metric (\k{appa},{\mu},{\nu})-manifolds under a condition which is given at Definition 3.1. We study properties of such manifolds according to the cases \k{appa}>-1, \k{appa}=-1, \k{appa}<-1 and construct new examples of such manifolds for each case.