Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2023; 38(4): 1271-1280

Online first article October 18, 2023      Printed October 31, 2023

Copyright © The Korean Mathematical Society.

on weakly cyclic generalized $B$-symmetric manifolds

Mohabbat Ali, Aziz Ullah Khan, Quddus Khan, Mohd Vasiulla

Jamia Millia Islamia; Jamia Millia Islamia; Jamia Millia Islamia; Jamia Millia Islamia


The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized $B$-symmetric manifold $(WCGBS)_{n}$. We obtain a sufficient condition for a weakly cyclic generalized $B$-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized $B$-symmetric manifolds. Then we study Einstein $(WCGBS)_{n}$ $(n>2)$. Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

Keywords: Generalized $B$-tensor, generalized quasi-Einstein manifold, Weyl semi-symmetry, conformally-flat manifold, generalized quasi-constant curvature, Einstein manifold

MSC numbers: Primary 53C15, 53C25