Open Access$ \ast $-Ricci tensor on $ (\kappa, \mu) $-contact manifolds
Author(s) -
Rongsheng Ma,
Donghe Pei
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022642
Subject(s) - kappa , ricci curvature , mathematics , ricci flow , invariant (physics) , pure mathematics , manifold (fluid mechanics) , mathematical analysis , combinatorics , mathematical physics , geometry , mechanical engineering , curvature , engineering
We introduce the notion of semi-symmetric $ \ast $-Ricci tensor and illustrate that a non-Sasakian $ (\kappa, \mu) $-contact manifold is $ \ast $-Ricci semi-symmetric or has parallel $ \ast $-Ricci operator if and only if it is $ \ast $-Ricci flat. Then we find that among the non-Sasakian $ (\kappa, \mu) $-contact manifolds with the same Boeckx invariant $ I_M $, only one is $ \ast $-Ricci flat, so we can think of it as the representative of such class. We also give two methods to construct $ \ast $-Ricci flat $ (\kappa, \mu) $-contact manifolds.