2025/09/26 by Galia Nakova, Nakova, Galia, Cornelia-Livia Bejan +1
Mathematics · Physics and Astronomy · #53C15 #53C50 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2509.21809
openalex publication_date 2025/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct and study almost paracontact metric structures (φ,ξ,η,g) on a 3-dimensional Walker manifold (M,g) with respect to a local basis only by the coordinate functions of a unit space-like vector field ξ, globally defined on M and a function f on M, characterizing the Lorentzian metric g. Necessary and sufficient conditions are obtained for M, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: paracontact metric, normal, almost α-paracosymplectic, almost paracosymplectic, paracosymplectic and \mathbbG12-manifolds. Also, classes to which the studied manifolds do not belong are found. Special attention is paid to an η-Einstein manifold among the considered manifolds and its ξ-sectional, φ-sectional and scalar curvature are investigated. Examples of the examined manifolds are given.