Open AccessA quarter-symmetric metric connection on almost contact B-metric manifolds
Author(s) -
Şenay Bulut
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/fil1916181b
Subject(s) - mathematics , metric connection , connection (principal bundle) , fundamental theorem of riemannian geometry , scalar curvature , riemann curvature tensor , metric (unit) , ricci curvature , manifold (fluid mechanics) , levi civita connection , pure mathematics , metric tensor , fubini–study metric , curvature , mathematical analysis , equivalence of metrics , ricci decomposition , injective metric space , fisher information metric , geometry , metric space , mechanical engineering , operations management , engineering , economics , geodesic
The aim of this paper is to study the notion of a quarter-symmetric metric connection on an almost contact B-metric manifold (M,?,?,?,g). We obtain the relation between the Levi-Civita connection and the quarter-symmetric metric connection on (M,?,?,?,g).We investigate the curvature tensor, Ricci tensor and scalar curvature tensor with respect to the quarter-symmetric metric connection. In case the manifold (M,?,?,?,g) is a Sasaki-like almost contact B-metric manifold, we get some formulas. Finally, we give some examples of a quarter-symmetric metric connection.