Open AccessCurvature properties of almost Ricci-like solitons with torse-forming vertical potential on almost contact b-metric manifolds
Author(s) -
Манчо Манев
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2108679m
Subject(s) - mathematics , ricci curvature , riemann curvature tensor , ricci decomposition , generalization , manifold (fluid mechanics) , metric (unit) , curvature , mathematical analysis , einstein manifold , curvature of riemannian manifolds , einstein tensor , pure mathematics , einstein , soliton , metric tensor , scalar curvature , mathematical physics , sectional curvature , geometry , physics , quantum mechanics , mechanical engineering , operations management , nonlinear system , economics , geodesic , engineering
A generalization of ?-Ricci solitons is considered involving an additional metric and functions as soliton coefficients. The soliton potential is torse-forming and orthogonal to the contact distribution of the almost contact B-metric manifold. Then such a manifold can also be considered as an almost Einstein like manifold, a generalization of an ?-Einstein manifold with respect to both B-metrics and functions as coefficients. Necessary and sufficient conditions are found for a number of properties of the curvature tensor and its Ricci tensor of the studied manifolds. Finally, an explicit example of an arbitrary dimension is given and some of the results are illustrated.