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

TL;DR

This paper investigates three-dimensional paracontact metric (ppa,race2,race3) manifolds, characterizing those with harmonic Reeb vector fields, analyzing curvature properties, and constructing new examples across different ppa cases.

Contribution

It provides a characterization of harmonic Reeb vector fields and introduces new examples of paracontact (ppa,race2,race3)-manifolds for various ppa values.

Findings

Characterization of harmonic Reeb vector fields in 3D paracontact manifolds

Analysis of curvature properties under specific conditions

Construction of new manifold examples for different ppa cases

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.