Open AccessGeometries of manifolds equipped with a Ricci (projection-Ricci) quarter-symmetric connection
Author(s) -
Wanxiao Tang,
Jon Yong Chol,
Ho Yun Tal,
Guangping He,
Peibiao Zhao
Publication year - 2019
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/fil1916237t
Subject(s) - ricci curvature , mathematics , curvature of riemannian manifolds , connection (principal bundle) , ricci flow , ricci decomposition , pure mathematics , manifold (fluid mechanics) , mathematical analysis , scalar curvature , topology (electrical circuits) , curvature , combinatorics , geometry , sectional curvature , mechanical engineering , engineering
We first introduce a Ricci quarter-symmetric connection and a projective Ricci quarter-symmetric connection, and then we investigate a Riemannian manifold admitting a Ricci (projective Ricci) quartersymmetric connection (M,g), and prove that a Riamannian manifold with a Ricci(projection-Ricci) quartersymmetric connection is of a constant curvature manifold. Furthermore, wederive that an Einstein manifold (M,g) is conformally flat under certain condition.