Open AccessTwo subclasses of generalized Kenmotsu manifolds
Author(s) -
A Abu-Saleem,
Ivan Kochetkov,
Aligadzhi Rustanov
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/918/1/012062
Subject(s) - riemann curvature tensor , pure mathematics , mathematics , manifold (fluid mechanics) , curvature , dimension (graph theory) , ricci flat manifold , class (philosophy) , metric (unit) , einstein manifold , mathematical analysis , ricci curvature , geometry , scalar curvature , computer science , operations management , artificial intelligence , economics , mechanical engineering , engineering
The paper studies the geometry of the Riemann curvature tensor of generalized Kenmotsu manifolds. In this paper, several identities satisfied by the curvature tensor of generalized Kenmotsu manifolds are obtained. Two identities are distinguished from the obtained identities, called the first and second additional identities of curvature of the GK-manifold. Based on additional identities, two subclasses of GK-manifolds are distinguished, and a local characterization of the distinguished classes is also obtained. It is proved that the distinguished two subclasses of GK-manifolds coincide and have dimension 5. In addition, it is proved that the class of distinguished manifolds coincides with the class of almost contact metric manifolds obtained from a cosymplectic manifold by a canonical concircular transformation of a cosymplectic structure of dimension 5.